NatProofs.mul_assoc: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as NatProofs
Lines 91-98 of bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&start_line=91&end_line=98

import Base

def mul_assoc(+a: Nat, +b: Nat, +c: Nat) -> {Nat.mul(Nat.mul(a, b), c) == Nat.mul(a, Nat.mul(b, c)) : Nat}:
  match a:
    case 0n:
      {==}
    case 1n+p:
      %Equal.sym(Nat, Nat.mul(Nat.add(b, Nat.mul(p, b)), c), Nat.add(Nat.mul(b, c), Nat.mul(Nat.mul(p, b), c)), mul_add_right(b, Nat.mul(p, b), c)) : {_ == Nat.mul(1n+p, Nat.mul(b, c)) : Nat}
      %Equal.sym(Nat, Nat.mul(Nat.mul(p, b), c), Nat.mul(p, Nat.mul(b, c)), mul_assoc(p, b, c)) : {Nat.add(Nat.mul(b, c), _) == Nat.mul(1n+p, Nat.mul(b, c)) : Nat}
      {==}

Uses (5):
  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=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&name=mul_add_right