NatAlgebra.mul_succ: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NatAlgebra
Lines 41-46 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&start_line=41&end_line=46

import Base

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

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=add_swap
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=succ_equal