def le_add_r

bend-collections-laws-crypto@1.0.0.0 · proofs/math/natural/logs.bend:14

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 A

14# a <= b gives a + c <= b + c
15def le_add_r(+a: Nat, +b: Nat, +c: Nat, +h: {Nat.is_le(a, b) == True{} : Bool}) -> {Nat.is_le(Nat.add(a, c), Nat.add(b, c)) == True{} : Bool}:
16  %Equal.sym(Nat, Nat.add(a, c), Nat.add(c, a), A.add_comm(a, c)) : {Nat.is_le(_, Nat.add(b, c)) == True{} : Bool}
17  %Equal.sym(Nat, Nat.add(b, c), Nat.add(c, b), A.add_comm(b, c)) : {Nat.is_le(Nat.add(c, a), _) == True{} : Bool}
18  N.le_add_left(a, b, c, h)