def succ_le

bend-collections-laws-math@1.0.0.0 · proofs/math/random/fround.bend:138

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

138def succ_le(+a: Nat, +b: Nat, +h: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_le(Nat.add(a, 1n), b) == True{} : Bool}:
139  L.subst(Nat, z => {Nat.is_le(z, b) == True{} : Bool}, 1n+a, Nat.add(a, 1n), Equal.sym(Nat, Nat.add(a, 1n), 1n+a, Equal.trans(Nat, Nat.add(a, 1n), Nat.add(1n, a), 1n+a, NA.add_comm(a, 1n), {==})), N.lt_succ_le_succ(a, b, h))