NatOrder.by_contra: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/nat_order.bend as NatOrder
Lines 233-241 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=233&end_line=241

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

# Proves x <= y from a refutation of y < x.
def by_contra(x: Nat, y: Nat, k: LE(1n+y, x) -> Empty) -> LE(x, y):
  match x y:
    case 0n y:
      MNat.zero_le(y)
    case 1n+xp 0n:
      Empty.absurd(LE(1n+xp, 0n), k(MNat.zero_le(xp)))
    case 1n+xp 1n+yp:
      by_contra(xp, yp, k)

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty
  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=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/nat.bend&name=zero_le