-- Generated by textbook/build_definitions.py -- hand-written Lean
-- definitions for concepts with no Mathlib equivalent. Regenerate
-- from the definitions manifest(s) instead of hand-editing.

import Mathlib

-- Definition 1.6.22: greatest common divisor (gcd) of several integers
-- No single ready-made Mathlib constant for 'gcd of a `List ℤ`' matches the book's definition verbatim, so this concept gets a real, hand-written Lean `def` (see lean_code) instead of only a JSON pointer -- it is compiled into textbook/lib/Definitions.lean by build_definitions.py and inlined into any statement's `prelude` that needs it, so Lean can actually elaborate proofs that use it, not just read a description of it.
def IsGCDOfList (d : ℕ) (as : List ℤ) : Prop :=
  (∀ a ∈ as, (d:ℤ) ∣ a) ∧ ∀ e : ℤ, (∀ a ∈ as, e ∣ a) → e ∣ (d:ℤ)