Gcd.dvd_gcd: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/gcd.bend as Gcd
Lines 125-126 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/gcd.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/gcd.bend&start_line=125&end_line=126

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

def dvd_gcd(+a: Nat, +b: Nat, +d: Nat, +ka: Nat, +kb: Nat, +ea: {a == Nat.mul(ka, d) : Nat}, +eb: {b == Nat.mul(kb, d) : Nat}) -> {M.gcd(a, b) == Nat.mul(dw(b, a, b, ka, kb), d) : Nat}:
  gcd_greatest(b, a, b, N.le_refl(b), d, ka, kb, ea, eb)

Uses (6):
  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/lib/nat.bend&name=le_refl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/gcd.bend&name=dw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/gcd.bend&name=gcd_greatest
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=gcd