Lists.gcd_all_dvd: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend as Lists
Lines 91-93 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&start_line=91&end_line=93

import Base
import bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend as M

# gcd_all(xs) divides every element: xs[i] == k gcd_all(xs) (0 past the end)   (Mathlib Finset.gcd_dvd)
def gcd_all_dvd(+xs: List<&2, Nat>, +i: Nat) -> {nth0(xs, i, 0n) == Nat.mul(gw_nth(xs, 0n, i), M.gcd_all(xs)) : Nat}:
  g_nth(xs, 0n, i)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=g_nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=gw_nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=nth0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=gcd_all