Nat.internal_div_le_wit: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 791-798 of bend-mathlib@0.8.1.0/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/nat.bend&start_line=791&end_line=798

import Base

def internal_div_le_wit(a: Nat, b: Nat, h: {Nat.is_le(a, b) == True{} : Bool}) -> &k:Nat -> {Nat.add(a, k) == b : Nat}:
  match a b:
    case 0n y:
      (y, {==})
    case 1n+ap 0n:
      Empty.absurd(&k:Nat -> {Nat.add(1n+ap, k) == 0n : Nat}, internal_false_ne_true(h))
    case 1n++ap 1n++bq:
      internal_div_wit_succ(ap, bq, internal_div_le_wit(ap, bq, h))

Uses (9):
  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=Exists
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_div_wit_succ
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_false_ne_true