Nat.internal_lt_of_not_le: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 2869-2874 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=2869&end_line=2874

import Base

def internal_lt_of_not_le(+a: Nat, +b: Nat, v: Bool, e: {v == Nat.is_lt(a, b) : Bool}, f: le(b, a) -> Empty) -> lt(a, b):
  match v:
    case True{}:
      Equal.sym(Bool, True{}, Nat.is_lt(a, b), e)
    case False{}:
      Empty.absurd(lt(a, b), f(le_of_not_lt(a, b, Equal.sym(Bool, False{}, Nat.is_lt(a, b), e))))

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
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le_of_not_lt
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt