Proof.gcd_all_greatest: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/proof.bend as Proof
Lines 68-69 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/proof.bend&start_line=68&end_line=69

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

def gcd_all_greatest(+d: Nat, +xs: List<&2, Nat>, +ks: List<&2, Nat>, h: S.dvd_with(d, xs, ks)) -> S.GcdAll.greatest(d, xs, ks, h):
  (LS.gw_dvd(xs, ks, 0n, 0n), LS.dvd_gcd_all(d, xs, ks, 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=Sigma
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=dvd_gcd_all
  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/spec/math/natural.bend&name=GcdAll.greatest
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/natural.bend&name=dvd_with