helm/software/matita/tests/ng_commands.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 include "nat/plus.ma".
  16
  17 ndefinition thesis0: ∀A:Type.Type ≝ λA. A → A.
  18
  19 alias id "thesis0" = "cic:/matita/tests/ng_commands/thesis0.def(0)".
  20
  21 ndefinition thesis: ∀A:Type.Type ≝ λA. ?.
  22  napply (A → A);
  23 nqed.
  24
  25 alias id "thesis" = "cic:/matita/tests/ng_commands/thesis.def(0)".
  26
  27 ntheorem foo: ∀A:Type.thesis A.#A;#x;napply x;
  28 nqed.
  29
  30 alias id "foo" = "cic:/matita/tests/ng_commands/foo.def(0)".
  31
  32 ntheorem goo: ∀A:Type.A → A. #A; napply (foo ?);
  33 nqed.
  34
  35 naxiom P: Prop.
  36
  37 alias id "P" = "cic:/matita/tests/ng_commands/P.decl".
  38
  39 ndefinition Q: Prop ≝ P.
  40
  41 nlet rec nzero (n:nat) : nat ≝
  42  match n with
  43   [ O ⇒ O
  44   | S m ⇒ nzero m].
  45
  46 alias id "nzero" = "cic:/matita/tests/ng_commands/nzero.fix(0,0,0)".
  47
  48 ntheorem nzero_ok: nzero (S (S O)) = O.
  49  napply (refl_eq ? O);
  50 nqed.
  51
  52 (*
  53 ninductive nnat: Type ≝
  54    nO: nnat
  55  | nS: nnat → nnat. *)