def lt_ne

bend-collections-laws-math@1.0.0.0 · proofs/lib/nat.bend:220

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

220def lt_ne(+a: Nat, +b: Nat, lt: {Nat.is_lt(a, b) == True{} : Bool}, e: {a == b : Nat}) -> Empty:
221  L.true_not_false(Nat.is_lt(a, a), Equal.trans(Bool, Nat.is_lt(a, a), Nat.is_lt(a, b), True{}, Equal.cong(Nat, Bool, x => Nat.is_lt(a, x), a, b, e), lt), lt_irrefl(a))