9341 lines
333 KiB
HTML
9341 lines
333 KiB
HTML
<!doctype html><html lang="en"><meta charset="utf-8"><title>P0 semantic simplex schemas</title><style>body{font:16px/1.5 system-ui;max-width:1050px;margin:32px auto;padding:16px}pre{white-space:pre-wrap;background:#f5f5f5;padding:16px}section{border-top:1px solid #ccc}</style><h1>65 semantic multi-role relation schemas</h1><p>Schema annotation seeds, not independently validated mathematical statements. A simplex joins the objects, assumptions and conclusion in its slots. References are partial symbol/syntax candidates. This review contains schema annotations and Lean signature text, not textbook passages or full assistant judgment explanations.</p><section id="P01"><h2>P01</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:548ab1a767a685aefa146455:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
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||
"reference_completeness": "partial"
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||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
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||
"kind": "object",
|
||
"context": "field",
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||
"attrs": {
|
||
"symbols": [],
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||
"keywords": [
|
||
"field"
|
||
],
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||
"introduced": "given",
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||
"quantifier_status": "unreviewed",
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||
"references": [],
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||
"reference_status": "unknown",
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||
"origin": "frozen_current_chat_annotation"
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||
}
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||
},
|
||
"fact1": {
|
||
"name": "fact1",
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||
"kind": "fact",
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||
"context": "commutative ring",
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||
"attrs": {
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||
"symbols": [],
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||
"keywords": [
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||
"commutative",
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||
"ring"
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||
],
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||
"introduced": "given",
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||
"quantifier_status": "unreviewed",
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||
"references": [],
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||
"reference_status": "unknown",
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||
"origin": "frozen_current_chat_annotation"
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||
}
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||
},
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"fact2": {
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||
"name": "fact2",
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||
"kind": "fact",
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||
"context": "identity nonzero",
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||
"attrs": {
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||
"symbols": [],
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||
"keywords": [
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||
"identity",
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||
"nonzero"
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||
],
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||
"introduced": "given",
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||
"quantifier_status": "unreviewed",
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||
"references": [],
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||
"reference_status": "unknown",
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||
"origin": "frozen_current_chat_annotation"
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||
}
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||
},
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"goal1": {
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"name": "goal1",
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"kind": "goal",
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"context": "nonzero elements are units",
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||
"attrs": {
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||
"symbols": [],
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||
"keywords": [
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"nonzero",
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||
"elements",
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||
"are",
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||
"units"
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||
],
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"introduced": "given",
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||
"quantifier_status": "unreviewed",
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||
"references": [],
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||
"reference_status": "unknown",
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"origin": "frozen_current_chat_annotation"
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}
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||
}
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||
}
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||
}</pre><h3>lean</h3><pre>{
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"name": "schema:p0-f12735802ba0:548ab1a767a685aefa146455:lean:v1",
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"kind": "simplex",
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"attrs": {
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"side": "lean",
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"reference_completeness": "syntactic_only"
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},
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"roles": {
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"F": {
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"name": "F",
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"kind": "object",
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||
"type": "Type*",
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"attrs": {
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"binder_kind": "explicit",
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"classified_by": "sort",
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"origin": "deterministic_signature_projection",
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"references": [],
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"reference_status": "syntactic_candidates"
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}
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},
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"own": {
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"name": "own",
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||
"kind": "own",
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||
"type": "class",
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||
"attrs": {
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||
"keyword": "class",
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||
"references": [],
|
||
"reference_status": "syntactic_candidates",
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||
"origin": "deterministic_signature_projection"
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||
}
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||
}
|
||
}
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}</pre></section><section id="P02"><h2>P02</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:6ea85a17cb5decb0670c4afe:source:v1",
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||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
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"roles": {
|
||
"object1": {
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||
"name": "G",
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||
"kind": "object",
|
||
"context": "group",
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||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
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||
}
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||
},
|
||
"object2": {
|
||
"name": "object2",
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||
"kind": "object",
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||
"context": "whole group",
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||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"whole",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "object3",
|
||
"kind": "object",
|
||
"context": "identity singleton",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"identity",
|
||
"singleton"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "both sets are subgroups",
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||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"both",
|
||
"sets",
|
||
"are",
|
||
"subgroups"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
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||
"origin": "frozen_current_chat_annotation"
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||
}
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||
}
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||
}
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||
}</pre><h3>lean</h3><pre>{
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||
"name": "schema:p0-f12735802ba0:6ea85a17cb5decb0670c4afe:lean:v1",
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"kind": "simplex",
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||
"attrs": {
|
||
"side": "lean",
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||
"reference_completeness": "syntactic_only"
|
||
},
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||
"roles": {
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||
"G": {
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||
"name": "G",
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||
"kind": "object",
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||
"type": "Type*",
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||
"attrs": {
|
||
"binder_kind": "explicit",
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||
"classified_by": "sort",
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||
"origin": "deterministic_signature_projection",
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||
"instances": [
|
||
"Group G"
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||
],
|
||
"references": [],
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||
"reference_status": "syntactic_candidates"
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||
}
|
||
},
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||
"goal": {
|
||
"name": "goal",
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||
"kind": "goal",
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||
"type": "Subgroup G (Set.univ : Set G) ∧ Subgroup G {1}",
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||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P03"><h2>P03</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:389a27cbae1957943fae2960:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "integer ring",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"integer",
|
||
"ring"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "unit",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"unit"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "units equal plus minus one",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"units",
|
||
"equal",
|
||
"plus",
|
||
"minus",
|
||
"one"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:389a27cbae1957943fae2960:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"premise1": {
|
||
"name": "premise1",
|
||
"kind": "fact",
|
||
"type": "(u : ℤ)",
|
||
"attrs": {
|
||
"binder_kind": "goal_implication",
|
||
"classified_by": "implication",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"premise2": {
|
||
"name": "premise2",
|
||
"kind": "fact",
|
||
"type": "IsUnit u",
|
||
"attrs": {
|
||
"binder_kind": "goal_implication",
|
||
"classified_by": "implication",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "u = 1 ∨ u = -1",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P04"><h2>P04</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:b63f0ed4d1ea1e11e34e6f8a:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "generated subgroup equals integer powers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"generated",
|
||
"subgroup",
|
||
"equals",
|
||
"integer",
|
||
"powers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:b63f0ed4d1ea1e11e34e6f8a:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\<a\\> = {a ^ k | k : ℤ}",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"a"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P05"><h2>P05</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:db4553333550bccbd3f0e21d:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "φ",
|
||
"kind": "object",
|
||
"context": "map between groups",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"map",
|
||
"between",
|
||
"groups"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "φ",
|
||
"kind": "fact",
|
||
"context": "bijective",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"bijective"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "φ",
|
||
"kind": "fact",
|
||
"context": "preserves multiplication",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"preserves",
|
||
"multiplication"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "isomorphic iff such map exists",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"isomorphic",
|
||
"iff",
|
||
"such",
|
||
"map",
|
||
"exists"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:db4553333550bccbd3f0e21d:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group H"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"own": {
|
||
"name": "own",
|
||
"kind": "own",
|
||
"type": "Prop",
|
||
"attrs": {
|
||
"keyword": "def",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P06"><h2>P06</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:c3e75089fbfe8f386b4a22ec:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"b"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "inverse product reverses inverse factors",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"inverse",
|
||
"product",
|
||
"reverses",
|
||
"inverse",
|
||
"factors"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:c3e75089fbfe8f386b4a22ec:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"b": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "(a * b)⁻¹ = b⁻¹ * a⁻¹",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"a",
|
||
"b"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P07"><h2>P07</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:91a6a0c1c21014bf08ffa3b6:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "integer modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"integer",
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "p",
|
||
"kind": "object",
|
||
"context": "prime factor",
|
||
"attrs": {
|
||
"symbols": [
|
||
"p"
|
||
],
|
||
"keywords": [
|
||
"prime",
|
||
"factor"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "q",
|
||
"kind": "object",
|
||
"context": "prime factor",
|
||
"attrs": {
|
||
"symbols": [
|
||
"q"
|
||
],
|
||
"keywords": [
|
||
"prime",
|
||
"factor"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "φ",
|
||
"kind": "object",
|
||
"context": "totient function",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"totient",
|
||
"function"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "φ",
|
||
"kind": "fact",
|
||
"context": "totient value can be found",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"totient",
|
||
"value",
|
||
"can",
|
||
"be",
|
||
"found"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object4"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "recover both prime factors",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"recover",
|
||
"both",
|
||
"prime",
|
||
"factors"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:91a6a0c1c21014bf08ffa3b6:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"p": {
|
||
"name": "p",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"q": {
|
||
"name": "q",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hn": {
|
||
"name": "hn",
|
||
"kind": "fact",
|
||
"type": "n = p * q",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n",
|
||
"p",
|
||
"q"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hpq": {
|
||
"name": "hpq",
|
||
"kind": "fact",
|
||
"type": "p.Prime ∧ q.Prime",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"p",
|
||
"q"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"premise1": {
|
||
"name": "premise1",
|
||
"kind": "fact",
|
||
"type": "∃ (φ : ℕ → ℕ), (∀ m, φ m = Nat.totient m)",
|
||
"attrs": {
|
||
"binder_kind": "goal_implication",
|
||
"classified_by": "implication",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "∃ (p' q' : ℕ), n = p' * q' ∧ p'.Prime ∧ q'.Prime",
|
||
"attrs": {
|
||
"exists_count": 1,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P08"><h2>P08</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:675ac9dbf3ec8a0553149a96:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "φ",
|
||
"kind": "object",
|
||
"context": "isomorphism",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "φ",
|
||
"kind": "fact",
|
||
"context": "group isomorphism",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "map preserves identity and inverses",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"map",
|
||
"preserves",
|
||
"identity",
|
||
"and",
|
||
"inverses"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:675ac9dbf3ec8a0553149a96:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group H"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "φ (1 : G) = (1 : H) ∧ ∀ g : G, φ g⁻¹ = (φ g)⁻¹",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 1,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G",
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P09"><h2>P09</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:8b39fc5b656bac00bc1e863f:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "cyclic group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"cyclic",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "rectangle symmetry group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"rectangle",
|
||
"symmetry",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object5": {
|
||
"name": "φ",
|
||
"kind": "object",
|
||
"context": "isomorphism",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object6": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object7": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "natural number",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"natural",
|
||
"number"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "nonisomorphism and preservation of powers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"nonisomorphism",
|
||
"and",
|
||
"preservation",
|
||
"of",
|
||
"powers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P10"><h2>P10</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:3549ad65eee67f7b432a8b70:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"b"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "left right equations uniquely solvable",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"left",
|
||
"right",
|
||
"equations",
|
||
"uniquely",
|
||
"solvable"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:3549ad65eee67f7b432a8b70:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"b": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\\\(∃! x : G, a * x = b) ∧ (∃! x : G, x * a = b)",
|
||
"attrs": {
|
||
"exists_count": 2,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G",
|
||
"a",
|
||
"b"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P11"><h2>P11</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:0b7db1a8100c33a50a08981f:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "group size",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"size"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "G",
|
||
"kind": "fact",
|
||
"context": "finite",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"finite"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "nth power equals identity",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"nth",
|
||
"power",
|
||
"equals",
|
||
"identity"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:0b7db1a8100c33a50a08981f:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G",
|
||
"Fintype G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"g": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "g ^ Fintype.card G = 1",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G",
|
||
"g"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P12"><h2>P12</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:e3d40d93cda13ec59c35d9a5:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "RSA method",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"rsa",
|
||
"method"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "messages",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"messages"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "design secure authenticated message exchange",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"design",
|
||
"secure",
|
||
"authenticated",
|
||
"message",
|
||
"exchange"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P13"><h2>P13</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:aaf1250a5104a4f7c1ca0d29:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "Φ",
|
||
"kind": "object",
|
||
"context": "group of units",
|
||
"attrs": {
|
||
"symbols": [
|
||
"Φ"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"of",
|
||
"units"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "a",
|
||
"kind": "fact",
|
||
"context": "relatively prime to modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"relatively",
|
||
"prime",
|
||
"to",
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "totient power congruent to one",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"totient",
|
||
"power",
|
||
"congruent",
|
||
"to",
|
||
"one"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:aaf1250a5104a4f7c1ca0d29:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h": {
|
||
"name": "h",
|
||
"kind": "fact",
|
||
"type": "Nat.Coprime a n",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "predicate",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"a",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "(a ^ Nat.totient n) ≡ 1 [ZMOD n]",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"a",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P14"><h2>P14</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:57966f39253aba58777a4ffd:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "X",
|
||
"kind": "object",
|
||
"context": "set",
|
||
"attrs": {
|
||
"symbols": [
|
||
"X"
|
||
],
|
||
"keywords": [
|
||
"set"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "real valued functions",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"real",
|
||
"valued",
|
||
"functions"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "ring identity and unit characterization",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"ring",
|
||
"identity",
|
||
"and",
|
||
"unit",
|
||
"characterization"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:57966f39253aba58777a4ffd:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"X": {
|
||
"name": "X",
|
||
"kind": "object",
|
||
"type": "Type",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "Ring (X → ℝ)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"X"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P15"><h2>P15</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:6ef921c49672c73f8f3e0edf:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "G",
|
||
"kind": "fact",
|
||
"context": "finite",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"finite"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "rows columns contain elements once",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"rows",
|
||
"columns",
|
||
"contain",
|
||
"elements",
|
||
"once"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:6ef921c49672c73f8f3e0edf:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G",
|
||
"Fintype G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"g": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h": {
|
||
"name": "h",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\\\\\n ∃! (x : G), x * g = h \\\\\\n ∧ ∃! (y : G), g * y = h",
|
||
"attrs": {
|
||
"exists_count": 2,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G",
|
||
"g",
|
||
"h"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P16"><h2>P16</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:371fe1b32fe04da354ad4478:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "K",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"K"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "object4",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "H",
|
||
"kind": "fact",
|
||
"context": "finite",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"finite"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "K",
|
||
"kind": "fact",
|
||
"context": "finite",
|
||
"attrs": {
|
||
"symbols": [
|
||
"K"
|
||
],
|
||
"keywords": [
|
||
"finite"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact3": {
|
||
"name": "G",
|
||
"kind": "fact",
|
||
"context": "isomorphic to product",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"isomorphic",
|
||
"to",
|
||
"product"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "element order divides lcm sizes",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"element",
|
||
"order",
|
||
"divides",
|
||
"lcm",
|
||
"sizes"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:371fe1b32fe04da354ad4478:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Fintype H",
|
||
"Group H"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"K": {
|
||
"name": "K",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Fintype K",
|
||
"Group K"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"g": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"type": "H × K",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"H",
|
||
"K"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "OrderOf g ∣ lcm (Fintype.card H) (Fintype.card K)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"H",
|
||
"K",
|
||
"g"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P17"><h2>P17</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:a7396b1a5d5ebcd5b48ea7ba:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "real numbers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"real",
|
||
"numbers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "rational numbers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"rational",
|
||
"numbers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "object3",
|
||
"kind": "object",
|
||
"context": "complex numbers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"complex",
|
||
"numbers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "object4",
|
||
"kind": "object",
|
||
"context": "integers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"integers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object5": {
|
||
"name": "object5",
|
||
"kind": "object",
|
||
"context": "real polynomial ring",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"real",
|
||
"polynomial",
|
||
"ring"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "three fields two nonfields",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"three",
|
||
"fields",
|
||
"two",
|
||
"nonfields"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P18"><h2>P18</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:59bb865c9bdfb8521e414743:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "complex numbers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"complex",
|
||
"numbers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "norm one subset",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"norm",
|
||
"one",
|
||
"subset"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "object3",
|
||
"kind": "object",
|
||
"context": "nonzero complex numbers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"nonzero",
|
||
"complex",
|
||
"numbers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "unit modulus set is subgroup",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"unit",
|
||
"modulus",
|
||
"set",
|
||
"is",
|
||
"subgroup"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P19"><h2>P19</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:283d407566264b02fbee6560:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "generated cyclic subgroup",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"generated",
|
||
"cyclic",
|
||
"subgroup"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "element order defined by subgroup size",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"element",
|
||
"order",
|
||
"defined",
|
||
"by",
|
||
"subgroup"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:283d407566264b02fbee6560:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"own": {
|
||
"name": "own",
|
||
"kind": "own",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"keyword": "def",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P20"><h2>P20</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:7de228e675b949cd64850c04:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "e",
|
||
"kind": "object",
|
||
"context": "identity element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"e"
|
||
],
|
||
"keywords": [
|
||
"identity",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "e'",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"e'"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "fact1",
|
||
"kind": "fact",
|
||
"context": "left product equals g",
|
||
"attrs": {
|
||
"symbols": [
|
||
"e'",
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"left",
|
||
"product",
|
||
"equals",
|
||
"g"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3",
|
||
"object4"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "element equals group identity",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"element",
|
||
"equals",
|
||
"group",
|
||
"identity"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:7de228e675b949cd64850c04:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"e'": {
|
||
"name": "e'",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"g": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h": {
|
||
"name": "h",
|
||
"kind": "fact",
|
||
"type": "e' * g = g",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"e'",
|
||
"g"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "e' = 1",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"e'"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P21"><h2>P21</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:dc1c450987f3e3a5285260f7:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "φ",
|
||
"kind": "object",
|
||
"context": "isomorphism",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "φ",
|
||
"kind": "fact",
|
||
"context": "group isomorphism",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "abelian iff target abelian",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"abelian",
|
||
"iff",
|
||
"target",
|
||
"abelian"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:dc1c450987f3e3a5285260f7:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group H"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\\\\\n Commutative (*) ↔ Commutative ((*) : H → H → H)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": true,
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P22"><h2>P22</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:c42dc687ecc042f5b7a00a9d:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "finite group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"finite",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "fact1",
|
||
"kind": "fact",
|
||
"context": "finite",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"finite"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "each row column permutes group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"each",
|
||
"row",
|
||
"column",
|
||
"permutes",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:c42dc687ecc042f5b7a00a9d:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Fintype G",
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\/\\n (∀ g : G, ∀ g' : G, ∃! h : G, g * h = g') ∧ \\/\\n (∀ g : G, ∀ g' : G, ∃! h : G, h * g = g')",
|
||
"attrs": {
|
||
"exists_count": 2,
|
||
"forall_count": 4,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P23"><h2>P23</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:8491370b02906b6efdb3da5e:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "natural modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"natural",
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "p",
|
||
"kind": "object",
|
||
"context": "prime",
|
||
"attrs": {
|
||
"symbols": [
|
||
"p"
|
||
],
|
||
"keywords": [
|
||
"prime"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "q",
|
||
"kind": "object",
|
||
"context": "prime",
|
||
"attrs": {
|
||
"symbols": [
|
||
"q"
|
||
],
|
||
"keywords": [
|
||
"prime"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "m",
|
||
"kind": "object",
|
||
"context": "integer exponent",
|
||
"attrs": {
|
||
"symbols": [
|
||
"m"
|
||
],
|
||
"keywords": [
|
||
"integer",
|
||
"exponent"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object5": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "n",
|
||
"kind": "fact",
|
||
"context": "product of primes",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"product",
|
||
"of",
|
||
"primes"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "m",
|
||
"kind": "fact",
|
||
"context": "lcm predecessors",
|
||
"attrs": {
|
||
"symbols": [
|
||
"m"
|
||
],
|
||
"keywords": [
|
||
"lcm",
|
||
"predecessors"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object4"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact3": {
|
||
"name": "a",
|
||
"kind": "fact",
|
||
"context": "relatively prime to modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"relatively",
|
||
"prime",
|
||
"to",
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object5"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "exponent power congruent to one",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"exponent",
|
||
"power",
|
||
"congruent",
|
||
"to",
|
||
"one"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:8491370b02906b6efdb3da5e:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"p": {
|
||
"name": "p",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"q": {
|
||
"name": "q",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hp": {
|
||
"name": "hp",
|
||
"kind": "fact",
|
||
"type": "Nat.Prime p",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "predicate",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"p"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hq": {
|
||
"name": "hq",
|
||
"kind": "fact",
|
||
"type": "Nat.Prime q",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "predicate",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"q"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hn": {
|
||
"name": "hn",
|
||
"kind": "fact",
|
||
"type": "n = p * q",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n",
|
||
"p",
|
||
"q"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"m": {
|
||
"name": "m",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hm": {
|
||
"name": "hm",
|
||
"kind": "fact",
|
||
"type": "m = Nat.lcm (p - 1) (q - 1)",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"m",
|
||
"p",
|
||
"q"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"ha": {
|
||
"name": "ha",
|
||
"kind": "fact",
|
||
"type": "Nat.Coprime a n",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "predicate",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"a",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "a ^ m ≡ 1 [ZMOD n]",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"a",
|
||
"m",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P24"><h2>P24</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:437d02fe69d580bde075648c:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "painted square",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"painted",
|
||
"square"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "color preserving symmetries",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"color",
|
||
"preserving",
|
||
"symmetries"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "identify symmetry group size isomorphism",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"identify",
|
||
"symmetry",
|
||
"group",
|
||
"size",
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P25"><h2>P25</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:5fe4f3fbbead7e6988f015a9:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "x",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"x"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "y",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"y"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "left and right cancellation implications",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"left",
|
||
"and",
|
||
"right",
|
||
"cancellation",
|
||
"implications"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:5fe4f3fbbead7e6988f015a9:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"x": {
|
||
"name": "x",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"y": {
|
||
"name": "y",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"premise1": {
|
||
"name": "premise1",
|
||
"kind": "fact",
|
||
"type": "a * x = a * y",
|
||
"attrs": {
|
||
"binder_kind": "goal_implication",
|
||
"classified_by": "implication",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"a",
|
||
"x",
|
||
"y"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "x = y",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"x",
|
||
"y"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P26"><h2>P26</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:8a55f59982e50e4af47b3d55:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "h",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"h"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "m",
|
||
"kind": "object",
|
||
"context": "exponent modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"m"
|
||
],
|
||
"keywords": [
|
||
"exponent",
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "h",
|
||
"kind": "fact",
|
||
"context": "congruent one modulo m",
|
||
"attrs": {
|
||
"symbols": [
|
||
"h"
|
||
],
|
||
"keywords": [
|
||
"congruent",
|
||
"one",
|
||
"modulo",
|
||
"m"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "power congruent to original integer",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"power",
|
||
"congruent",
|
||
"to",
|
||
"original",
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:8a55f59982e50e4af47b3d55:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h": {
|
||
"name": "h",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"m": {
|
||
"name": "m",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hn": {
|
||
"name": "hn",
|
||
"kind": "fact",
|
||
"type": "h % m = 1",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"h",
|
||
"m"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hm": {
|
||
"name": "hm",
|
||
"kind": "fact",
|
||
"type": "m ∣ n",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"m",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "a ^ h ≡ a [ZMOD n]",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"a",
|
||
"h",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P27"><h2>P27</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:8d4d64143a8b214e38d7ba1b:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "S_4",
|
||
"kind": "object",
|
||
"context": "permutation group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"S_4"
|
||
],
|
||
"keywords": [
|
||
"permutation",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "π",
|
||
"kind": "object",
|
||
"context": "permutation",
|
||
"attrs": {
|
||
"symbols": [
|
||
"π"
|
||
],
|
||
"keywords": [
|
||
"permutation"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "object3",
|
||
"kind": "object",
|
||
"context": "stabilizer subgroup",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"stabilizer",
|
||
"subgroup"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "π",
|
||
"kind": "fact",
|
||
"context": "fixes fourth point",
|
||
"attrs": {
|
||
"symbols": [
|
||
"π"
|
||
],
|
||
"keywords": [
|
||
"fixes",
|
||
"fourth",
|
||
"point"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "stabilizer subgroup isomorphic to S3",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"stabilizer",
|
||
"subgroup",
|
||
"isomorphic",
|
||
"to",
|
||
"s"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P28"><h2>P28</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:6017927fdafd91ca22ed6ade:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "rational number",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"rational",
|
||
"number"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"context": "rational number",
|
||
"attrs": {
|
||
"symbols": [
|
||
"b"
|
||
],
|
||
"keywords": [
|
||
"rational",
|
||
"number"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "object3",
|
||
"kind": "object",
|
||
"context": "real quadratic subset",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"real",
|
||
"quadratic",
|
||
"subset"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "object4",
|
||
"kind": "object",
|
||
"context": "conjugation map",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"conjugation",
|
||
"map"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "subset field conjugation is automorphism",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"subset",
|
||
"field",
|
||
"conjugation",
|
||
"is",
|
||
"automorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P29"><h2>P29</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:089c452ec2f9b850733a44f6:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "φ",
|
||
"kind": "object",
|
||
"context": "isomorphism",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object5": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "natural number",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"natural",
|
||
"number"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "φ",
|
||
"kind": "fact",
|
||
"context": "group isomorphism",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "map preserves powers and identity powers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"map",
|
||
"preserves",
|
||
"powers",
|
||
"and",
|
||
"identity"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:089c452ec2f9b850733a44f6:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group H"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"g": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\/\\/ φ(g^n) = (φ g)^n ∧ (g^n = 1 → (φ g)^n = 1)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"g",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P30"><h2>P30</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:75009c3d616f02be4d7a5824:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "M",
|
||
"kind": "object",
|
||
"context": "set",
|
||
"attrs": {
|
||
"symbols": [
|
||
"M"
|
||
],
|
||
"keywords": [
|
||
"set"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "N",
|
||
"kind": "object",
|
||
"context": "subset",
|
||
"attrs": {
|
||
"symbols": [
|
||
"N"
|
||
],
|
||
"keywords": [
|
||
"subset"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "sequence of elements",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"sequence",
|
||
"of",
|
||
"elements"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "M",
|
||
"kind": "fact",
|
||
"context": "associative operation",
|
||
"attrs": {
|
||
"symbols": [
|
||
"M"
|
||
],
|
||
"keywords": [
|
||
"associative",
|
||
"operation"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "N",
|
||
"kind": "fact",
|
||
"context": "closed under multiplication",
|
||
"attrs": {
|
||
"symbols": [
|
||
"N"
|
||
],
|
||
"keywords": [
|
||
"closed",
|
||
"under",
|
||
"multiplication"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact3": {
|
||
"name": "n",
|
||
"kind": "fact",
|
||
"context": "positive",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"positive"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact4": {
|
||
"name": "a",
|
||
"kind": "fact",
|
||
"context": "elements belong to subset",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"elements",
|
||
"belong",
|
||
"to",
|
||
"subset"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object4"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "ordered product belongs to subset",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"ordered",
|
||
"product",
|
||
"belongs",
|
||
"to",
|
||
"subset"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:75009c3d616f02be4d7a5824:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"M": {
|
||
"name": "M",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Semigroup M"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"N": {
|
||
"name": "N",
|
||
"kind": "object",
|
||
"type": "Set M",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"M"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hN": {
|
||
"name": "hN",
|
||
"kind": "fact",
|
||
"type": "∀ x y ∈ N, x * y ∈ N",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"N"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hn": {
|
||
"name": "hn",
|
||
"kind": "fact",
|
||
"type": "1 ≤ n",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "Fin n → M",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"M",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"ha": {
|
||
"name": "ha",
|
||
"kind": "fact",
|
||
"type": "∀ i, a i ∈ N",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"N",
|
||
"a"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "(∏ i, a i) ∈ N",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"N",
|
||
"a"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P31"><h2>P31</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:9091f6a277215174e821d373:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "φ",
|
||
"kind": "object",
|
||
"context": "previously defined ring map",
|
||
"attrs": {
|
||
"symbols": [
|
||
"φ"
|
||
],
|
||
"keywords": [
|
||
"previously",
|
||
"defined",
|
||
"ring",
|
||
"map"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "verify this map preserves ring operations",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"verify",
|
||
"this",
|
||
"map",
|
||
"preserves",
|
||
"ring"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:9091f6a277215174e821d373:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"R": {
|
||
"name": "R",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Ring R"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"S": {
|
||
"name": "S",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Ring S"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "IsRingHom φ",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P32"><h2>P32</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:0cd2f0368a0d8234c2593845:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "matrix size",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"matrix",
|
||
"size"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "T",
|
||
"kind": "object",
|
||
"context": "real matrix",
|
||
"attrs": {
|
||
"symbols": [
|
||
"T"
|
||
],
|
||
"keywords": [
|
||
"real",
|
||
"matrix"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "evaluation at matrix is homomorphism",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"evaluation",
|
||
"at",
|
||
"matrix",
|
||
"is",
|
||
"homomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:0cd2f0368a0d8234c2593845:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"T": {
|
||
"name": "T",
|
||
"kind": "object",
|
||
"type": "Matrix n n ℝ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "RingHom (Polynomial ℝ) (Matrix n n ℝ)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P33"><h2>P33</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:8e55e625fa9b10b7b65f59f4:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "G",
|
||
"kind": "fact",
|
||
"context": "four elements",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"four",
|
||
"elements"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "nonidentity element squares to identity",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"nonidentity",
|
||
"element",
|
||
"squares",
|
||
"to",
|
||
"identity"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:8e55e625fa9b10b7b65f59f4:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hG": {
|
||
"name": "hG",
|
||
"kind": "fact",
|
||
"type": "Fintype.card G = 4",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "∃ g : G, g ≠ 1 ∧ g * g = 1",
|
||
"attrs": {
|
||
"exists_count": 1,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P34"><h2>P34</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:534c6ffcf56931559e70657b:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "S_3",
|
||
"kind": "object",
|
||
"context": "symmetric group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"S_3"
|
||
],
|
||
"keywords": [
|
||
"symmetric",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "cyclic group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"cyclic",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "nonabelian and abelian hence nonisomorphic",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"nonabelian",
|
||
"and",
|
||
"abelian",
|
||
"hence",
|
||
"nonisomorphic"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P35"><h2>P35</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:aa16561dceee591e35e42c4d:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "M",
|
||
"kind": "object",
|
||
"context": "set",
|
||
"attrs": {
|
||
"symbols": [
|
||
"M"
|
||
],
|
||
"keywords": [
|
||
"set"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "M",
|
||
"kind": "fact",
|
||
"context": "associative operation",
|
||
"attrs": {
|
||
"symbols": [
|
||
"M"
|
||
],
|
||
"keywords": [
|
||
"associative",
|
||
"operation"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "n",
|
||
"kind": "fact",
|
||
"context": "positive",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"positive"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "unique coherent associative product family",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"unique",
|
||
"coherent",
|
||
"associative",
|
||
"product",
|
||
"family"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:aa16561dceee591e35e42c4d:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"M": {
|
||
"name": "M",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Semigroup M"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h": {
|
||
"name": "h",
|
||
"kind": "fact",
|
||
"type": "n ≥ 1",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"premise1": {
|
||
"name": "premise1",
|
||
"kind": "fact",
|
||
"type": "∃! f : (Fin n → M)",
|
||
"attrs": {
|
||
"binder_kind": "goal_implication",
|
||
"classified_by": "implication",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"M",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "M, (∀ a : M, f ![a] = a) ∧ (∀ a b : M, f ![a, b] = a * b) ∧ (∀ (k : ℕ) (hk : 1 ≤ k) (hnk : k < n) (a : Fin n → M), f a = f (a ↾ k) * f (a ∘ (Fin.succAbove k).symm))",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 3,
|
||
"is_iff": false,
|
||
"references": [
|
||
"M",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P36"><h2>P36</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:73ec95bfac2896218d2b1dab:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "C_n",
|
||
"kind": "object",
|
||
"context": "root of unity group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"C_n"
|
||
],
|
||
"keywords": [
|
||
"root",
|
||
"of",
|
||
"unity",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "order",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"order"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "ξ",
|
||
"kind": "object",
|
||
"context": "complex exponential generator",
|
||
"attrs": {
|
||
"symbols": [
|
||
"ξ"
|
||
],
|
||
"keywords": [
|
||
"complex",
|
||
"exponential",
|
||
"generator"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "cyclic with specified order generator",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"cyclic",
|
||
"with",
|
||
"specified",
|
||
"order",
|
||
"generator"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:73ec95bfac2896218d2b1dab:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h": {
|
||
"name": "h",
|
||
"kind": "fact",
|
||
"type": "n > 0",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "IsCyclic (ZMod n)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P37"><h2>P37</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:6b5a55ec3bb3c85239919649:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "C_n",
|
||
"kind": "object",
|
||
"context": "root of unity set",
|
||
"attrs": {
|
||
"symbols": [
|
||
"C_n"
|
||
],
|
||
"keywords": [
|
||
"root",
|
||
"of",
|
||
"unity",
|
||
"set"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "k",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"k"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "k",
|
||
"kind": "fact",
|
||
"context": "between zero and n minus one",
|
||
"attrs": {
|
||
"symbols": [
|
||
"k"
|
||
],
|
||
"keywords": [
|
||
"between",
|
||
"zero",
|
||
"and",
|
||
"n",
|
||
"minus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "roots equal specified exponential set",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"roots",
|
||
"equal",
|
||
"specified",
|
||
"exponential",
|
||
"set"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:6b5a55ec3bb3c85239919649:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"own": {
|
||
"name": "own",
|
||
"kind": "own",
|
||
"type": "Subgroup ℂ",
|
||
"attrs": {
|
||
"keyword": "def",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P38"><h2>P38</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:d6ddc1df3ce6b764f3fb8d73:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "subset",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"subset"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "H",
|
||
"kind": "fact",
|
||
"context": "nonempty",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"nonempty"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "H",
|
||
"kind": "fact",
|
||
"context": "closed under products",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"closed",
|
||
"under",
|
||
"products"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact3": {
|
||
"name": "H",
|
||
"kind": "fact",
|
||
"context": "closed under inverses",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"closed",
|
||
"under",
|
||
"inverses"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "conditions imply subgroup and identity",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"conditions",
|
||
"imply",
|
||
"subgroup",
|
||
"and",
|
||
"identity"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:d6ddc1df3ce6b764f3fb8d73:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Set G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h_one": {
|
||
"name": "h_one",
|
||
"kind": "fact",
|
||
"type": "∀ h ∈ H, h⁻¹ ∈ H",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h_mul": {
|
||
"name": "h_mul",
|
||
"kind": "fact",
|
||
"type": "∀ h1 h2 ∈ H, h1 * h2 ∈ H",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "IsSubgroup H",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P39"><h2>P39</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:ed87589326312890bea42d7c:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "K",
|
||
"kind": "object",
|
||
"context": "field",
|
||
"attrs": {
|
||
"symbols": [
|
||
"K"
|
||
],
|
||
"keywords": [
|
||
"field"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "Laurent polynomials",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"laurent",
|
||
"polynomials"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "ring with identity and units",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"ring",
|
||
"with",
|
||
"identity",
|
||
"and",
|
||
"units"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:ed87589326312890bea42d7c:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"K": {
|
||
"name": "K",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Field K"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "Ring (LaurentSeries K)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"K"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P40"><h2>P40</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:d609c5bb746fc0e05625134a:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "f",
|
||
"kind": "object",
|
||
"context": "map",
|
||
"attrs": {
|
||
"symbols": [
|
||
"f"
|
||
],
|
||
"keywords": [
|
||
"map"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "object3",
|
||
"kind": "object",
|
||
"context": "integers",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"integers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "object4",
|
||
"kind": "object",
|
||
"context": "residue ring",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"residue",
|
||
"ring"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "canonical residue map is homomorphism",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"canonical",
|
||
"residue",
|
||
"map",
|
||
"is",
|
||
"homomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:d609c5bb746fc0e05625134a:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "RingHom ℤ (ZMod n)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P41"><h2>P41</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:4405f31187373d5e1de622d2:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "natural number",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"natural",
|
||
"number"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "S_n",
|
||
"kind": "object",
|
||
"context": "symmetric group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"S_n"
|
||
],
|
||
"keywords": [
|
||
"symmetric",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "factorial cardinality always nonabelian when n≥3",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"factorial",
|
||
"cardinality",
|
||
"always",
|
||
"nonabelian",
|
||
"when"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:4405f31187373d5e1de622d2:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hn": {
|
||
"name": "hn",
|
||
"kind": "fact",
|
||
"type": "n ≥ 3",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\n Fintype.card (Symmetric n) = n! ∧ ¬ IsAbelian (Symmetric n)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P42"><h2>P42</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:05a6defa23576b7da41f8fbf:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "subset",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"subset"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "H",
|
||
"kind": "fact",
|
||
"context": "nonempty",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"nonempty"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "H",
|
||
"kind": "fact",
|
||
"context": "subgroup",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"subgroup"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "product closure is necessary",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"product",
|
||
"closure",
|
||
"is",
|
||
"necessary"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:05a6defa23576b7da41f8fbf:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Set G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h_nonempty": {
|
||
"name": "h_nonempty",
|
||
"kind": "object",
|
||
"type": "H.Nonempty",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h_prod": {
|
||
"name": "h_prod",
|
||
"kind": "fact",
|
||
"type": "∀ h1 h2 ∈ H, h1 * h2 ∈ H",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "IsSubgroup H",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P43"><h2>P43</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:47c39e88c29e3974e8864e90:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "fact1",
|
||
"kind": "fact",
|
||
"context": "order two",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"order",
|
||
"two"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "unique group up to isomorphism",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"unique",
|
||
"group",
|
||
"up",
|
||
"to",
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:47c39e88c29e3974e8864e90:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G",
|
||
"Fintype G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Type",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group H",
|
||
"Fintype H"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hG": {
|
||
"name": "hG",
|
||
"kind": "fact",
|
||
"type": "Fintype.card G = 2",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hH": {
|
||
"name": "hH",
|
||
"kind": "fact",
|
||
"type": "Fintype.card H = 2",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "Nonempty (G ≃* H)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G",
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P44"><h2>P44</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:fa61f8cb0e88b11e158c4eec:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"b"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "abelian defined by commuting products",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"abelian",
|
||
"defined",
|
||
"by",
|
||
"commuting",
|
||
"products"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:fa61f8cb0e88b11e158c4eec:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"own": {
|
||
"name": "own",
|
||
"kind": "own",
|
||
"type": "Prop",
|
||
"attrs": {
|
||
"keyword": "class",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P45"><h2>P45</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:3c00c37b39285cbd7d0be732:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "fact1",
|
||
"kind": "fact",
|
||
"context": "order three",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"order",
|
||
"three"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "unique group up to isomorphism",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"unique",
|
||
"group",
|
||
"up",
|
||
"to",
|
||
"isomorphism"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P46"><h2>P46</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:186d922a4121917ac8643316:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "real three variable polynomials",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"real",
|
||
"three",
|
||
"variable",
|
||
"polynomials"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "ring identity and unit characterization",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"ring",
|
||
"identity",
|
||
"and",
|
||
"unit",
|
||
"characterization"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P47"><h2>P47</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:e845a95d7b5054a0dbdf34eb:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "d",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"d"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "generated subgroup",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"generated",
|
||
"subgroup"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "integer multiples cyclic opposite generators equal",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"integer",
|
||
"multiples",
|
||
"cyclic",
|
||
"opposite",
|
||
"generators"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:e845a95d7b5054a0dbdf34eb:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"d": {
|
||
"name": "d",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "(Submodule.span ℤ {d}) = {n * d | n : ℤ}",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"d"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P48"><h2>P48</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:e7a3cec23c2ecdc655dd12cf:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "h",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"h"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "fact1",
|
||
"kind": "fact",
|
||
"context": "product equals identity",
|
||
"attrs": {
|
||
"symbols": [
|
||
"h",
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"product",
|
||
"equals",
|
||
"identity"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2",
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "left inverse equals inverse element",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"left",
|
||
"inverse",
|
||
"equals",
|
||
"inverse",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:e7a3cec23c2ecdc655dd12cf:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h": {
|
||
"name": "h",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"g": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hg": {
|
||
"name": "hg",
|
||
"kind": "fact",
|
||
"type": "h * g = 1",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"g",
|
||
"h"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "h = g⁻¹",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"g",
|
||
"h"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P49"><h2>P49</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:e966f3b17e32318acd5f2762:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"g"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "inverse of inverse equals element",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"inverse",
|
||
"of",
|
||
"inverse",
|
||
"equals",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:e966f3b17e32318acd5f2762:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"g": {
|
||
"name": "g",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "g = (g⁻¹)⁻¹",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"g"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P50"><h2>P50</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:2c420bf6ec32069ecd0043dc:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "R",
|
||
"kind": "object",
|
||
"context": "set",
|
||
"attrs": {
|
||
"symbols": [
|
||
"R"
|
||
],
|
||
"keywords": [
|
||
"set"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "addition",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"addition"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "object3",
|
||
"kind": "object",
|
||
"context": "multiplication",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"multiplication"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "R",
|
||
"kind": "fact",
|
||
"context": "nonempty",
|
||
"attrs": {
|
||
"symbols": [
|
||
"R"
|
||
],
|
||
"keywords": [
|
||
"nonempty"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "ring defined by additive group associativity distributivity",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"ring",
|
||
"defined",
|
||
"by",
|
||
"additive",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:2c420bf6ec32069ecd0043dc:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"R": {
|
||
"name": "R",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"own": {
|
||
"name": "own",
|
||
"kind": "own",
|
||
"type": "structure",
|
||
"attrs": {
|
||
"keyword": "structure",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P51"><h2>P51</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:25af34567cb2040bf41869e5:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "C_4",
|
||
"kind": "object",
|
||
"context": "fourth roots",
|
||
"attrs": {
|
||
"symbols": [
|
||
"C_4"
|
||
],
|
||
"keywords": [
|
||
"fourth",
|
||
"roots"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "complex multiplication",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"complex",
|
||
"multiplication"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "specified roots form group with identity",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"specified",
|
||
"roots",
|
||
"form",
|
||
"group",
|
||
"with"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P52"><h2>P52</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:578ae89f353ecbdc0ffb76a2:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "K",
|
||
"kind": "object",
|
||
"context": "field",
|
||
"attrs": {
|
||
"symbols": [
|
||
"K"
|
||
],
|
||
"keywords": [
|
||
"field"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "polynomials over field",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"polynomials",
|
||
"over",
|
||
"field"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "commutative ring identity units constant",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"commutative",
|
||
"ring",
|
||
"identity",
|
||
"units",
|
||
"constant"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:578ae89f353ecbdc0ffb76a2:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"K": {
|
||
"name": "K",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Field K"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\\\[isCommutativeRing (Polynomial K) ∧ (1 : Polynomial K) = 1 ∧ ∀ p : Polynomial K, IsUnit p → ∃ a : K, p = C a := by \\\\- sorry",
|
||
"attrs": {
|
||
"exists_count": 1,
|
||
"forall_count": 1,
|
||
"is_iff": false,
|
||
"references": [
|
||
"K"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P53"><h2>P53</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:1a8d6a5c9aa3cc5000dee474:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "group order is cardinality",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"group",
|
||
"order",
|
||
"is",
|
||
"cardinality"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:1a8d6a5c9aa3cc5000dee474:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G",
|
||
"Fintype G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"own": {
|
||
"name": "own",
|
||
"kind": "own",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"keyword": "def",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P54"><h2>P54</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:450c7df89ecd284b0e08504a:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "d",
|
||
"kind": "object",
|
||
"context": "residue",
|
||
"attrs": {
|
||
"symbols": [
|
||
"d"
|
||
],
|
||
"keywords": [
|
||
"residue"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "object3",
|
||
"kind": "object",
|
||
"context": "generated cyclic subgroup",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"generated",
|
||
"cyclic",
|
||
"subgroup"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "subgroup equals integer and residue multiples",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"subgroup",
|
||
"equals",
|
||
"integer",
|
||
"and",
|
||
"residue"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:450c7df89ecd284b0e08504a:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"d": {
|
||
"name": "d",
|
||
"kind": "object",
|
||
"type": "ℕ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hn": {
|
||
"name": "hn",
|
||
"kind": "fact",
|
||
"type": "0 < n",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\\\\\n (ZMod n).subgroup.closure ({ZMod.mk d} : Set (ZMod n)) = \\\\\\n {ZMod.mk (k * d % n) | k : ℤ} = \\\\\\n {ZMod.mk (k * d % n) | k : ZMod n}",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"d",
|
||
"n"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P55"><h2>P55</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:f908ac15b1bf8228281bcf68:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "first group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"first",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "second group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"second",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "fact1",
|
||
"kind": "fact",
|
||
"context": "groups are isomorphic",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"groups",
|
||
"are",
|
||
"isomorphic"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "abelian properties equivalent",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"abelian",
|
||
"properties",
|
||
"equivalent"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:f908ac15b1bf8228281bcf68:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group H"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"iso": {
|
||
"name": "iso",
|
||
"kind": "fact",
|
||
"type": "G ≃* H",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G",
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "(IsAbelian G ↔ IsAbelian H)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": true,
|
||
"references": [
|
||
"G",
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P56"><h2>P56</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:bcdfa01447e7060e1fd3d935:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "RSA method",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"rsa",
|
||
"method"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "message",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"message"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "design message authentication method",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"design",
|
||
"message",
|
||
"authentication",
|
||
"method"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P57"><h2>P57</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:f86421f93f1381d2ce728bc1:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "R",
|
||
"kind": "object",
|
||
"context": "ring",
|
||
"attrs": {
|
||
"symbols": [
|
||
"R"
|
||
],
|
||
"keywords": [
|
||
"ring"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "S",
|
||
"kind": "object",
|
||
"context": "ring",
|
||
"attrs": {
|
||
"symbols": [
|
||
"S"
|
||
],
|
||
"keywords": [
|
||
"ring"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "f",
|
||
"kind": "object",
|
||
"context": "map",
|
||
"attrs": {
|
||
"symbols": [
|
||
"f"
|
||
],
|
||
"keywords": [
|
||
"map"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "ring element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"ring",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object5": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"context": "ring element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"b"
|
||
],
|
||
"keywords": [
|
||
"ring",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "homomorphism preserves operations bijective means isomorphism",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"homomorphism",
|
||
"preserves",
|
||
"operations",
|
||
"bijective",
|
||
"means"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:f86421f93f1381d2ce728bc1:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"R": {
|
||
"name": "R",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Ring R"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"S": {
|
||
"name": "S",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Ring S"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"f": {
|
||
"name": "f",
|
||
"kind": "object",
|
||
"type": "R → S",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"R",
|
||
"S"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "Function.IsRingHom f ↔ (∀ a b : R, f (a + b) = f a + f b ∧ f (a * b) = f a * f b)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 1,
|
||
"is_iff": true,
|
||
"references": [
|
||
"R",
|
||
"f"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P58"><h2>P58</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:89fe687db9136379cd276fff:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "cyclic group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"cyclic",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "rectangle symmetry group",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"rectangle",
|
||
"symmetry",
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "nonisomorphic groups of order four",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"nonisomorphic",
|
||
"groups",
|
||
"of",
|
||
"order",
|
||
"four"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P59"><h2>P59</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:da65aa56505f6c13e6553d0d:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"context": "subset",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"subset"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "H",
|
||
"kind": "fact",
|
||
"context": "nonempty",
|
||
"attrs": {
|
||
"symbols": [
|
||
"H"
|
||
],
|
||
"keywords": [
|
||
"nonempty"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "subgroup iff group under inherited operation",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"subgroup",
|
||
"iff",
|
||
"group",
|
||
"under",
|
||
"inherited"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:da65aa56505f6c13e6553d0d:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"H": {
|
||
"name": "H",
|
||
"kind": "object",
|
||
"type": "Set G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h_nonempty": {
|
||
"name": "h_nonempty",
|
||
"kind": "object",
|
||
"type": "H.Nonempty",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "Subgroup.of G H ↔ IsGroup (H, (*), 1, ⁻¹)",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": true,
|
||
"references": [
|
||
"G",
|
||
"H"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P60"><h2>P60</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:ab2990e9786d5bda5a04e067:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "T",
|
||
"kind": "object",
|
||
"context": "map",
|
||
"attrs": {
|
||
"symbols": [
|
||
"T"
|
||
],
|
||
"keywords": [
|
||
"map"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "three dimensional space",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"three",
|
||
"dimensional",
|
||
"space"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "T",
|
||
"kind": "fact",
|
||
"context": "bijective",
|
||
"attrs": {
|
||
"symbols": [
|
||
"T"
|
||
],
|
||
"keywords": [
|
||
"bijective"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "T",
|
||
"kind": "fact",
|
||
"context": "continuous first partial derivatives",
|
||
"attrs": {
|
||
"symbols": [
|
||
"T"
|
||
],
|
||
"keywords": [
|
||
"continuous",
|
||
"first",
|
||
"partial",
|
||
"derivatives"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "diffeomorphisms form group under composition",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"diffeomorphisms",
|
||
"form",
|
||
"group",
|
||
"under",
|
||
"composition"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:ab2990e9786d5bda5a04e067:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"U": {
|
||
"name": "U",
|
||
"kind": "object",
|
||
"type": "Set (ℝ × ℝ × ℝ)",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"hU": {
|
||
"name": "hU",
|
||
"kind": "fact",
|
||
"type": "IsOpen U",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "predicate",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"U"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\\\\\n Group (Subtype (fun T : (ℝ × ℝ × ℝ) → (ℝ × ℝ × ℝ) => \\\\\\n Bijective T ∧ DifferentiableOn ℝ T U ∧ ContinuousOn (fun x => deriv (T ∘ (Prod.fst, Prod.snd, Prod.third)) x) U))",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"U"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P61"><h2>P61</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:a892779bfcaca35b91e7d611:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "T",
|
||
"kind": "object",
|
||
"context": "map",
|
||
"attrs": {
|
||
"symbols": [
|
||
"T"
|
||
],
|
||
"keywords": [
|
||
"map"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "three dimensional space",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"three",
|
||
"dimensional",
|
||
"space"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "T",
|
||
"kind": "fact",
|
||
"context": "bijective",
|
||
"attrs": {
|
||
"symbols": [
|
||
"T"
|
||
],
|
||
"keywords": [
|
||
"bijective"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "T",
|
||
"kind": "fact",
|
||
"context": "continuous",
|
||
"attrs": {
|
||
"symbols": [
|
||
"T"
|
||
],
|
||
"keywords": [
|
||
"continuous"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact3": {
|
||
"name": "T",
|
||
"kind": "fact",
|
||
"context": "inverse continuous",
|
||
"attrs": {
|
||
"symbols": [
|
||
"T"
|
||
],
|
||
"keywords": [
|
||
"inverse",
|
||
"continuous"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "homeomorphisms form group under composition",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"homeomorphisms",
|
||
"form",
|
||
"group",
|
||
"under",
|
||
"composition"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section><section id="P62"><h2>P62</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:7593062cab7c74cdecec08d0:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "a",
|
||
"kind": "fact",
|
||
"context": "finite order",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"finite",
|
||
"order"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object1"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "least positive exponent bounded powers generate",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"least",
|
||
"positive",
|
||
"exponent",
|
||
"bounded",
|
||
"powers"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:7593062cab7c74cdecec08d0:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"ha": {
|
||
"name": "ha",
|
||
"kind": "fact",
|
||
"type": "IsOfFinOrder a",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "predicate",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"a"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "\\/\\/ (orderOf a = (min {n : ℕ | n > 0 ∧ a ^ n = 1})) ∧ (Subgroup.closure ({a} : Set G) = {a ^ k | k : ℕ, k < orderOf a})",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"G",
|
||
"a"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P63"><h2>P63</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:c8204e9d19a6dd5d730dccc7:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"context": "group",
|
||
"attrs": {
|
||
"symbols": [
|
||
"G"
|
||
],
|
||
"keywords": [
|
||
"group"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "e",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"e"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "e'",
|
||
"kind": "object",
|
||
"context": "group element",
|
||
"attrs": {
|
||
"symbols": [
|
||
"e'"
|
||
],
|
||
"keywords": [
|
||
"group",
|
||
"element"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "e",
|
||
"kind": "fact",
|
||
"context": "two sided identity",
|
||
"attrs": {
|
||
"symbols": [
|
||
"e"
|
||
],
|
||
"keywords": [
|
||
"two",
|
||
"sided",
|
||
"identity"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact2": {
|
||
"name": "e'",
|
||
"kind": "fact",
|
||
"context": "two sided identity",
|
||
"attrs": {
|
||
"symbols": [
|
||
"e'"
|
||
],
|
||
"keywords": [
|
||
"two",
|
||
"sided",
|
||
"identity"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object3"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "two identities equal",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"two",
|
||
"identities",
|
||
"equal"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:c8204e9d19a6dd5d730dccc7:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"G": {
|
||
"name": "G",
|
||
"kind": "object",
|
||
"type": "Type*",
|
||
"attrs": {
|
||
"binder_kind": "implicit",
|
||
"classified_by": "sort",
|
||
"origin": "deterministic_signature_projection",
|
||
"instances": [
|
||
"Group G"
|
||
],
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"e": {
|
||
"name": "e",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"e'": {
|
||
"name": "e'",
|
||
"kind": "object",
|
||
"type": "G",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h_e": {
|
||
"name": "h_e",
|
||
"kind": "fact",
|
||
"type": "∀ g : G, e * g = g ∧ g * e = g",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G",
|
||
"e"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h_e'": {
|
||
"name": "h_e'",
|
||
"kind": "fact",
|
||
"type": "∀ g : G, e' * g = g ∧ g * e' = g",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"G",
|
||
"e'"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "e = e'",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"e",
|
||
"e'"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P64"><h2>P64</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:b40279b634fffd0841ff0f5a:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": false,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"a"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"context": "integer",
|
||
"attrs": {
|
||
"symbols": [
|
||
"b"
|
||
],
|
||
"keywords": [
|
||
"integer"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object3": {
|
||
"name": "r",
|
||
"kind": "object",
|
||
"context": "exponent",
|
||
"attrs": {
|
||
"symbols": [
|
||
"r"
|
||
],
|
||
"keywords": [
|
||
"exponent"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object4": {
|
||
"name": "s",
|
||
"kind": "object",
|
||
"context": "exponent",
|
||
"attrs": {
|
||
"symbols": [
|
||
"s"
|
||
],
|
||
"keywords": [
|
||
"exponent"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object5": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"context": "modulus",
|
||
"attrs": {
|
||
"symbols": [
|
||
"n"
|
||
],
|
||
"keywords": [
|
||
"modulus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"fact1": {
|
||
"name": "b",
|
||
"kind": "fact",
|
||
"context": "congruent to power modulo n",
|
||
"attrs": {
|
||
"symbols": [
|
||
"b"
|
||
],
|
||
"keywords": [
|
||
"congruent",
|
||
"to",
|
||
"power",
|
||
"modulo",
|
||
"n"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [
|
||
"object2"
|
||
],
|
||
"reference_status": "explicit_symbol_candidates",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "ciphertext power returns original residue",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"ciphertext",
|
||
"power",
|
||
"returns",
|
||
"original",
|
||
"residue"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:b40279b634fffd0841ff0f5a:lean:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "lean",
|
||
"reference_completeness": "syntactic_only"
|
||
},
|
||
"roles": {
|
||
"a": {
|
||
"name": "a",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"b": {
|
||
"name": "b",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"r": {
|
||
"name": "r",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"s": {
|
||
"name": "s",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"n": {
|
||
"name": "n",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"t": {
|
||
"name": "t",
|
||
"kind": "object",
|
||
"type": "ℤ",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "default",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h1": {
|
||
"name": "h1",
|
||
"kind": "fact",
|
||
"type": "b ≡ a^r [ZMOD n]",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"a",
|
||
"b",
|
||
"n",
|
||
"r"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"h2": {
|
||
"name": "h2",
|
||
"kind": "fact",
|
||
"type": "r * s = 1 + n * t",
|
||
"attrs": {
|
||
"binder_kind": "explicit",
|
||
"classified_by": "relation",
|
||
"origin": "deterministic_signature_projection",
|
||
"references": [
|
||
"n",
|
||
"r",
|
||
"s",
|
||
"t"
|
||
],
|
||
"reference_status": "syntactic_candidates"
|
||
}
|
||
},
|
||
"goal": {
|
||
"name": "goal",
|
||
"kind": "goal",
|
||
"type": "b^s ≡ a [ZMOD n]",
|
||
"attrs": {
|
||
"exists_count": 0,
|
||
"forall_count": 0,
|
||
"is_iff": false,
|
||
"references": [
|
||
"a",
|
||
"b",
|
||
"n",
|
||
"s"
|
||
],
|
||
"reference_status": "syntactic_candidates",
|
||
"origin": "deterministic_signature_projection"
|
||
}
|
||
}
|
||
}
|
||
}</pre></section><section id="P65"><h2>P65</h2><h3>source</h3><pre>{
|
||
"name": "schema:p0-f12735802ba0:f8d2e206681972927560be2c:source:v1",
|
||
"kind": "simplex",
|
||
"attrs": {
|
||
"side": "source",
|
||
"goal_has_exists": true,
|
||
"reference_completeness": "partial"
|
||
},
|
||
"roles": {
|
||
"object1": {
|
||
"name": "object1",
|
||
"kind": "object",
|
||
"context": "nonsquare rhombus",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"nonsquare",
|
||
"rhombus"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"object2": {
|
||
"name": "object2",
|
||
"kind": "object",
|
||
"context": "geometric symmetries",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"geometric",
|
||
"symmetries"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
},
|
||
"goal1": {
|
||
"name": "goal1",
|
||
"kind": "goal",
|
||
"context": "identify symmetry group size and classification",
|
||
"attrs": {
|
||
"symbols": [],
|
||
"keywords": [
|
||
"identify",
|
||
"symmetry",
|
||
"group",
|
||
"size",
|
||
"and"
|
||
],
|
||
"introduced": "given",
|
||
"quantifier_status": "unreviewed",
|
||
"references": [],
|
||
"reference_status": "unknown",
|
||
"origin": "frozen_current_chat_annotation"
|
||
}
|
||
}
|
||
}
|
||
}</pre><h3>lean</h3><pre>Insufficient projected roles; no object roles were invented.</pre></section></html> |