Gcd.step_both: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/gcd.bend as Gcd
Lines 68-73 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/gcd.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/gcd.bend&start_line=68&end_line=73

import Base

def step_both(+bp: Nat, +a: Nat, +g: Nat, w: Wit, ih: divides_both(1n+bp, Nat.mod(a, 1n+bp), g, w)) -> divides_both(a, 1n+bp, g, wstep(Nat.div(a, 1n+bp), w)):
  match w:
    case W{+l, +r}:
      (en, er) = ih
      +en2 = {en : {1n+bp == Nat.mul(l, g) : Nat}}
      (dvd_of_mod(bp, a, g, l, r, en2, er), en2)

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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/gcd.bend&name=Wit
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/gcd.bend&name=divides_both
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/gcd.bend&name=dvd_of_mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/gcd.bend&name=wstep