NatProofs.mul_succ_right: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as NatProofs
Lines 52-59 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=52&end_line=59

import Base

def mul_succ_right(+a: Nat, +q: Nat) -> {Nat.mul(a, 1n+q) == Nat.add(a, Nat.mul(a, q)) : Nat}:
  match a:
    case 0n:
      {==}
    case 1n+p:
      %Equal.sym(Nat, Nat.mul(p, 1n+q), Nat.add(p, Nat.mul(p, q)), mul_succ_right(p, q)) : {1n+Nat.add(q, _) == 1n+Nat.add(p, Nat.add(q, Nat.mul(p, q))) : Nat}
      %add_swap(q, p, Nat.mul(p, q)) : {1n+Nat.add(q, Nat.add(p, Nat.mul(p, q))) == 1n+_ : 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=add_swap