Stuff moved from old Matita.

[helm.git] / matita / matita / tests / ng_commands.ma

diff --git a/matita/matita/tests/ng_commands.ma b/matita/matita/tests/ng_commands.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ng_pts.ma".
+
+ndefinition thesis0: ∀A:Type.Type ≝ λA. A → A.
+
+ndefinition thesis: ∀A:Type.Type ≝ λA. ?.
+ napply (A → A);
+nqed.
+
+ntheorem foo: ∀A:Type.thesis A.#A;#x;napply x;
+nqed.
+
+ntheorem goo: ∀A:Type.A → A. #A; napply (foo ?);
+nqed.
+
+naxiom NP: Prop.
+
+ndefinition Q: Prop ≝ NP.
+
+include "nat/nat.ma".
+
+nlet rec nzero (n:nat) : nat ≝
+ match n with
+  [ O ⇒ O
+  | S m ⇒ nzero m].
+
+ntheorem nzero_ok: nzero (S (S O)) = O.
+ napply (refl_eq ? O);
+nqed.
+
+naxiom DT: nat → Type.
+naxiom dt: ∀n. DT n.
+
+ninductive nnat (n: nat) (A:DT n): Type ≝
+   nO: nnat n A
+ | nS: mat n A → mat n A → nnat n A
+with mat: Type ≝ 
+ |mS : nnat n A → mat n A.
+
+nlet rec nnzero (n:nnat 0 (dt ?)) : nnat 0 (dt ?) ≝
+ match n return ? with
+  [ nO ⇒ nO 0 (dt ?)
+  | nS m _ ⇒ nmzero m ]
+and nmzero (m:mat 0 (dt ?)) : nnat 0 (dt ?) ≝ 
+ match m return ? with
+ [ mS n ⇒ nnzero n ].
+
+nrecord pair (n: nat) (x: DT n) (label: Type): Type ≝
+ { lbl:label; l: pair n x label; r: pair n x label}.