Nat.internal_div_zero_of_wit: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 807-811 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=807&end_line=811

import Base

def internal_div_zero_of_wit(+a: Nat, +b: Nat, w: &k:Nat -> {Nat.add(a, k) == b : Nat}) -> {Nat.div(a, 1n+b) == 0n : Nat}:
  match w:
    case (+k, e):
      %e : {Nat.div(a, 1n+_) == 0n : Nat}
      Equal.sym(Nat, 0n, Pair.fst(Nat, Nat, Nat.divmod.go(a, Nat.add(a, k), 0n, 0n)), internal_div_go_small(a, k, 0n, 0n))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.divmod.go
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.fst
  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_go_small