Sort.internal_le_flip_nat: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/sort.bend as Sort
Lines 41-50 of bend-mathlib@0.8.1.0/sort.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/sort.bend&start_line=41&end_line=50

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

def internal_le_flip_nat(x: Nat, y: Nat, e: {Nat.is_le(x, y) == False{} : Bool}) -> {Nat.is_le(y, x) == True{} : Bool}:
  match x y:
    case 0n 0n:
      Empty.absurd({True{} == True{} : Bool}, MNat.internal_false_ne_true(Equal.sym(Bool, True{}, False{}, e)))
    case 0n 1n+q:
      Empty.absurd({Nat.is_le(1n+q, 0n) == True{} : Bool}, MNat.internal_false_ne_true(Equal.sym(Bool, True{}, False{}, e)))
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      internal_le_flip_nat(p, q, e)

Uses (6):
  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=Equal.sym
  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_le
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_false_ne_true