Egcd.spread: 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 41-45 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=41&end_line=45

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A

# (q b + r) y == b (q y) + r y
def spread(+q: Nat, +b: Nat, +r: Nat, +y: Nat) -> {Nat.mul(Nat.add(Nat.mul(q, b), r), y) == Nat.add(Nat.mul(b, Nat.mul(q, y)), Nat.mul(r, y)) : Nat}:
  %Equal.sym(Nat, Nat.mul(Nat.add(Nat.mul(q, b), r), y), Nat.add(Nat.mul(Nat.mul(q, b), y), Nat.mul(r, y)), A.mul_add_right(Nat.mul(q, b), r, y)) : {_ == Nat.add(Nat.mul(b, Nat.mul(q, y)), Nat.mul(r, y)) : Nat}
  %Equal.sym(Nat, Nat.mul(Nat.mul(q, b), y), Nat.mul(b, Nat.mul(q, y)), qby(q, b, y)) : {Nat.add(_, Nat.mul(r, y)) == Nat.add(Nat.mul(b, Nat.mul(q, y)), Nat.mul(r, y)) : Nat}
  {==}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_add_right
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/egcd.bend&name=qby