NatOrder.gt_le: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/nat_order.bend as NatOrder
Lines 213-222 of bend-kit-collections@0.1.4.1/nat_order.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&start_line=213&end_line=222

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

def gt_le(a: Nat, b: Nat, e: {Nat.is_gt(a, b) == True{} : Bool}) -> LE(1n+b, a):
  match a b:
    case 0n 0n:
      Empty.absurd(LE(1n, 0n), MBool.false_ne_true()(e))
    case 0n 1n+bp:
      Empty.absurd(LE(1n+1n+bp, 0n), MBool.false_ne_true()(e))
    case 1n+ap 0n:
      MNat.zero_le(ap)
    case 1n+ap 1n+bp:
      gt_le(ap, bp, e)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_gt
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=LE
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=false_ne_true
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=zero_le