def add_lt2

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64light.bend:66

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/math/typed/width.bend as WW

66def add_lt2(+a: Nat, +b: Nat, +h: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_lt(Nat.add(a, a), Nat.add(b, b)) == True{} : Bool}:
67  +l1 = Equal.trans(Bool, Nat.is_lt(Nat.add(a, a), Nat.add(a, b)), Nat.is_lt(a, b), True{}, WW.lt_cancel_l(a, a, b), h)
68  +l2 = Equal.trans(Bool, Nat.is_lt(Nat.add(a, b), Nat.add(b, b)), Nat.is_lt(a, b), True{}, WW.lt_cancel_r(a, b, b), h)
69  N.lt_trans(Nat.add(a, a), Nat.add(a, b), Nat.add(b, b), l1, l2)