def gt_le

bend-kit-collections@0.1.4.1 · nat_order.bend:213

import Base
import bend-mathlib@0.7.4.0/nat.bend as MNat
import bend-mathlib@0.7.4.0/bool.bend as MBool

213def gt_le(a: Nat, b: Nat, e: {Nat.is_gt(a, b) == True{} : Bool}) -> LE(1n+b, a):
214  match a b:
215    case 0n 0n:
216      Empty.absurd(LE(1n, 0n), MBool.false_ne_true()(e))
217    case 0n 1n+bp:
218      Empty.absurd(LE(1n+1n+bp, 0n), MBool.false_ne_true()(e))
219    case 1n+ap 0n:
220      MNat.zero_le(ap)
221    case 1n+ap 1n+bp:
222      gt_le(ap, bp, e)