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def le_add2

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/ineq.bend:29

import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as Ineq
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

29# a <= c, b <= d: a + b <= c + d
30def le_add2(+a: Nat, +b: Nat, +c: Nat, +d: Nat, +h1: {Nat.is_le(a, c) == True{} : Bool}, +h2: {Nat.is_le(b, d) == True{} : Bool}) -> {Nat.is_le(Nat.add(a, b), Nat.add(c, d)) == True{} : Bool}:
31  N.le_trans(Nat.add(a, b), Nat.add(c, b), Nat.add(c, d), WW.le_add_r(a, c, b, h1), N.le_add_left(b, d, c, h2))

Uses (7)

Used by (4)