helm/software/matita/tests/ng_commands.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* ATTENZIONE: si puo' eseguire solo con MatitaC e dopo aver scelto
  16    Debug → always show all disambiguation errors (that, moreover, slows
  17    down the library a lot) *)
  18
  19 include "nat/plus.ma".
  20
  21 ndefinition thesis0: ∀A:Type.Type ≝ λA. A → A.
  22
  23 ndefinition thesis: ∀A:Type.Type ≝ λA. ?.
  24  napply (A → A);
  25 nqed.
  26
  27 ntheorem foo: ∀A:Type.thesis A.#A;#x;napply x;
  28 nqed.
  29
  30 ntheorem goo: ∀A:Type.A → A. #A; napply (foo ?);
  31 nqed.
  32
  33 naxiom NP: Prop.
  34
  35 ndefinition Q: Prop ≝ NP.
  36
  37 nlet rec nzero (n:nat) : nat ≝
  38  match n with
  39   [ O ⇒ O
  40   | S m ⇒ nzero m].
  41
  42 ntheorem nzero_ok: nzero (S (S O)) = O.
  43  napply (refl_eq ? O);
  44 nqed.
  45
  46 (*
  47 ninductive nnat: Type ≝
  48    nO: nnat
  49  | nS: nnat → nnat. *)