Proof.gcd_all_divides: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend as Proof
Lines 65-66 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend&start_line=65&end_line=66

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend as LS

def gcd_all_divides(+xs: List<&2, Nat>, +i: Nat) -> S.GcdAll.divides(xs, i):
  (LS.gw_nth(xs, 0n, i), LS.gcd_all_dvd(xs, i))

Uses (6):
  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=Sigma
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&name=gcd_all_dvd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&name=gw_nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=GcdAll.divides