def le_not_lt

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/nat.bend:173

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

173def le_not_lt(+a: Nat, +b: Nat, e: {Nat.is_le(b, a) == True{} : Bool}) -> {Nat.is_lt(a, b) == False{} : Bool}:
174  match a b:
175    case _ 0n:
176      not_lt_zero(a)
177    case 0n 1n+q:
178      Empty.absurd({Nat.is_lt(0n, 1n+q) == False{} : Bool}, L.false_true(e))
179    case 1n+p 1n+q:
180      le_not_lt(p, q, e)