NatProofs.mul_add_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 83-89 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=83&end_line=89

import Base
import bendtorch-core@0.1.0.0/src/shape/index_proofs.bend as Index

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

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/index_proofs.bend&name=add_assoc