Nat.internal_div_not_succ_le: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 909-916 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=909&end_line=916

import Base

def internal_div_not_succ_le(a: Nat, bp: Nat, h: {False{} == Nat.is_le(1n+bp, a) : Bool}) -> {Nat.is_le(a, bp) == True{} : Bool}:
  match a bp:
    case 0n q:
      Equal.sym(Bool, True{}, Nat.is_le(0n, q), internal_div_zero_le(q))
    case 1n+ap 0n:
      Empty.absurd({Nat.is_le(1n+ap, 0n) == True{} : Bool}, internal_div_true_ne_false(Equal.sym(Bool, False{}, True{}, Equal.trans(Bool, False{}, Nat.is_le(0n, ap), True{}, h, Equal.sym(Bool, True{}, Nat.is_le(0n, ap), internal_div_zero_le(ap))))))
    case 1n+ap 1n+q:
      internal_div_not_succ_le(ap, q, h)

Uses (8):
  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=Equal.trans
  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_div_true_ne_false
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_div_zero_le