def internal_div_le_wit

bend-mathlib@0.8.1.0 · nat.bend:791

import Base

791def internal_div_le_wit(a: Nat, b: Nat, h: {Nat.is_le(a, b) == True{} : Bool}) -> &k:Nat -> {Nat.add(a, k) == b : Nat}:
792  match a b:
793    case 0n y:
794      (y, {==})
795    case 1n+ap 0n:
796      Empty.absurd(&k:Nat -> {Nat.add(1n+ap, k) == 0n : Nat}, internal_false_ne_true(h))
797    case 1n++ap 1n++bq:
798      internal_div_wit_succ(ap, bq, internal_div_le_wit(ap, bq, h))