def lt_add_pos

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/ineq.bend:77

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

77# 0 < b: a < a + b
78def lt_add_pos(+a: Nat, +b: Nat, +h: {Nat.is_lt(0n, b) == True{} : Bool}) -> {Nat.is_lt(a, Nat.add(a, b)) == True{} : Bool}:
79  +s = N.lt_add_left(0n, b, a, h)
80  lt_subst_l(Nat.add(a, 0n), a, Nat.add(a, b), NA.add_zero(a), s)