def mul_add_right

bendtorch-core@0.1.0.0 · src/shape/nat_proofs.bend:83

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

83def 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}:
84  match a:
85    case 0n:
86      {==}
87    case 1n+p:
88      %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}
89      Index.add_assoc(c, Nat.mul(p, c), Nat.mul(b, c))