Semiring.mul_swap: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend as Semiring
Lines 21-25 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend&start_line=21&end_line=25

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

def mul_swap(+a: Nat, +b: Nat, +c: Nat) -> {Nat.mul(a, Nat.mul(b, c)) == Nat.mul(b, Nat.mul(a, c)) : Nat}:
  %NA.mul_assoc(a, b, c) : {_ == Nat.mul(b, Nat.mul(a, c)) : Nat}
  %NA.mul_assoc(b, a, c) : {Nat.mul(Nat.mul(a, b), c) == _ : Nat}
  %NA.mul_comm(a, b) : {Nat.mul(Nat.mul(a, b), c) == Nat.mul(_, c) : Nat}
  {==}

Uses (4):
  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/lemmas/proofs/nat_algebra.bend&name=mul_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_comm