Egcd.up_gcd: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/number/egcd.bend as Egcd
Lines 16-19 of bend-collections-laws-math@1.0.0.0/proofs/math/number/egcd.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/egcd.bend&start_line=16&end_line=19

import Base
import bend-collections-laws-math@1.0.0.0/src/math/number.bend as NB
import bend-collections-laws-math@1.0.0.0/spec/math/number.bend as SN

def up_gcd(+q: Nat, r: NB.EGcd) -> {SN.eg_gcd(NB.eg_up(q, r)) == SN.eg_gcd(r) : Nat}:
  match r:
    case NB.EG{+g, +x, +y, +neg}:
      {==}

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/number.bend&name=eg_gcd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/number.bend&name=EGcd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/number.bend&name=eg_up