def le_lt_add

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/ineq.bend:37

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/math/typed/width.bend as WW

37# a <= c, b < d: a + b < c + d
38def le_lt_add(+a: Nat, +b: Nat, +c: Nat, +d: Nat, +h1: {Nat.is_le(a, c) == True{} : Bool}, +h2: {Nat.is_lt(b, d) == True{} : Bool}) -> {Nat.is_lt(Nat.add(a, b), Nat.add(c, d)) == True{} : Bool}:
39  N.le_lt_trans(Nat.add(a, b), Nat.add(c, b), Nat.add(c, d), WW.le_add_r(a, c, b, h1), N.lt_add_left(b, d, c, h2))