def le_add_r

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/num.bend:72

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

72# x <= a -> x + y <= a + y
73def le_add_r(+x: Nat, +a: Nat, +y: Nat, +h: {Nat.is_le(x, a) == True{} : Bool}) -> {Nat.is_le(Nat.add(x, y), Nat.add(a, y)) == True{} : Bool}:
74  +e1 = N.le_add_left(x, a, y, h)
75  %NA.add_comm(y, x) : {Nat.is_le(_, Nat.add(a, y)) == True{} : Bool}
76  %NA.add_comm(y, a) : {Nat.is_le(Nat.add(y, x), _) == True{} : Bool}
77  e1