Egcd.base: 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 64-68 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=64&end_line=68

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

# the base case: a * 1 == a + b * 0
def base(+a: Nat, +b: Nat) -> {Nat.mul(a, 1n) == Nat.add(a, Nat.mul(b, 0n)) : Nat}:
  %Equal.sym(Nat, Nat.mul(a, 1n), a, A.mul_one(a)) : {_ == Nat.add(a, Nat.mul(b, 0n)) : Nat}
  %Equal.sym(Nat, Nat.mul(b, 0n), 0n, A.mul_zero(b)) : {a == Nat.add(a, _) : Nat}
  Equal.sym(Nat, Nat.add(a, 0n), a, A.add_zero(a))

Uses (7):
  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=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_zero