matita/matita/tests/bad_induction.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15
  16
  17 include "nat/nat.ma".
  18
  19 include "logic/equality.ma".
  20
  21 axiom bad_ind : ∀P : nat -> Prop. ∀n.(n = O -> P n) -> (∀n.P n -> P (S n)) -> P n.
  22
  23 theorem absurd: ∀n. n = O.
  24   intros.
  25   letin P ≝ (λx:nat. n = O).
  26   apply (bad_ind P n); simplify; intros; unfold; autobatch.
  27 qed.