def lt_not_le

bend-collections-laws-math@1.0.0.0 · proofs/lib/nat.bend:182

import Base

182def lt_not_le(+a: Nat, +b: Nat, e: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_le(b, a) == False{} : Bool}:
183  match a b:
184    case _ 0n:
185      Empty.absurd({Nat.is_le(0n, a) == False{} : Bool}, lt_zero_absurd(a, e))
186    case 0n 1n+q:
187      {==}
188    case 1n+p 1n+q:
189      lt_not_le(p, q, e)