def add_comm
bendtorch-core@0.1.0.0 · src/tensor/signed_PROOF.bend:67
import bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend as SignedPROOF
import Base
67def add_comm(+a: Nat, +b: Nat) -> {Nat.add(a, b) == Nat.add(b, a) : Nat}:
68 match a:
69 case 0n:
70 Equal.sym(Nat, Nat.add(b, 0n), b, add_zero_right(b))
71 case 1n+p:
72 Equal.trans(Nat, 1n+Nat.add(p, b), 1n+Nat.add(b, p), Nat.add(b, 1n+p),
73 Equal.cong(Nat, Nat, x => 1n+x, Nat.add(p, b), Nat.add(b, p), add_comm(p, b)),
74 Equal.sym(Nat, Nat.add(b, 1n+p), 1n+Nat.add(b, p), add_succ_right(b, p)))