def pred_succ

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/negate.bend:36

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

36# (B - 1) + 1 = B
37def pred_succ(+b: Nat, +h: {Nat.is_le(1n, b) == True{} : Bool}) -> {Nat.add(Nat.sub(b, 1n), 1n) == b : Nat}:
38  %Equal.sym(Nat, Nat.add(Nat.sub(b, 1n), 1n), Nat.add(1n, Nat.sub(b, 1n)), NA.add_comm(Nat.sub(b, 1n), 1n)) : {_ == b : Nat}
39  N.sub_add(b, 1n, h)