matita/tests/discriminate.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 set "baseuri" "cic:/matita/tests/discriminate".
  16 include "legacy/coq.ma".
  17 alias id "not" = "cic:/Coq/Init/Logic/not.con".
  18 alias num (instance 0) = "natural number".
  19 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
  20
  21 inductive foo: Prop \def I_foo: foo.
  22
  23 theorem stupid:
  24   1 = 0 \to (\forall p:Prop. p \to not p).
  25   intros.
  26   generalize in match I_foo.
  27   discriminate H.
  28 qed.
  29
  30 inductive bar_list (A:Set): Set \def
  31   | bar_nil: bar_list A
  32   | bar_cons: A \to bar_list A \to bar_list A.
  33
  34 alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
  35 theorem stupid2:
  36   \forall A:Set.\forall x:A.\forall l:bar_list A.
  37   bar_nil A = bar_cons A x l \to False.
  38   intros.
  39   discriminate H.
  40 qed.