U32.internal_fin_exact: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 272-278 of bend-mathlib@0.8.1.0/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/u32.bend&start_line=272&end_line=278

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

def internal_fin_exact(+e: Nat, +s: Nat, +m: Nat, o: Bool, eq: {Nat.add(e, Bool.pick(Nat, o, m, 0n)) == s : Nat}, h: MNat.lt(s, m)) -> {e == s : Nat}:
  match o:
    case False{}:
      Equal.trans(Nat, e, Nat.add(e, 0n), s, MNat.add_zero_sym(e), eq)
    case True{}:
      +le = MNat.le_of_add_eq(m, e, s, Equal.trans(Nat, Nat.add(m, e), Nat.add(e, m), s, MNat.add_comm(m, e), eq))
      Empty.absurd({e == s : Nat}, MNat.lt_irrefl(s)(MNat.lt_of_lt_of_le(s, m, s, h, le)))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.pick
  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.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.add
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_zero_sym
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le_of_add_eq
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt_irrefl
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt_of_lt_of_le