Lists.dvd_gcd_all: 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 119-121 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=119&end_line=121

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

# every common divisor of the elements divides gcd_all(xs)   (Mathlib Finset.dvd_gcd)
def dvd_gcd_all(+d: Nat, +xs: List<&2, Nat>, +ks: List<&2, Nat>, h: dvd_with(d, xs, ks)) -> {M.gcd_all(xs) == Nat.mul(gw_dvd(xs, ks, 0n, 0n), d) : Nat}:
  g_dvd(d, xs, ks, 0n, 0n, {==}, h)

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=dvd_with
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=g_dvd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=gw_dvd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=gcd_all