def sc_add

bend-collections-laws-math@1.0.0.0 · proofs/lib/u32alg.bend:47

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

47def sc_add(+n: Nat, +x: Nat, +y: Nat) -> {Nat.add(sc(n, x), sc(n, y)) == sc(n, Nat.add(x, y)) : Nat}:
48  match n:
49    case 0n:
50      {==}
51    case 1n+p:
52      %Equal.sym(Nat, Nat.add(Nat.double(sc(p, x)), Nat.double(sc(p, y))), Nat.double(Nat.add(sc(p, x), sc(p, y))), N.add_double(sc(p, x), sc(p, y))) : {_ == Nat.double(sc(p, Nat.add(x, y))) : Nat}
53      Equal.cong(Nat, Nat, Nat.double, Nat.add(sc(p, x), sc(p, y)), sc(p, Nat.add(x, y)), sc_add(p, x, y))