(* *)
(**************************************************************************)
-include "nat/plus.ma".
+include "ng_pts.ma".
ndefinition thesis0: ∀A:Type.Type ≝ λA. A → A.
-alias id "thesis0" = "cic:/matita/tests/ng_commands/thesis0.def(0)".
-
ndefinition thesis: ∀A:Type.Type ≝ λA. ?.
napply (A → A);
nqed.
-alias id "thesis" = "cic:/matita/tests/ng_commands/thesis.def(0)".
-
ntheorem foo: ∀A:Type.thesis A.#A;#x;napply x;
nqed.
-alias id "foo" = "cic:/matita/tests/ng_commands/foo.def(0)".
-
ntheorem goo: ∀A:Type.A → A. #A; napply (foo ?);
nqed.
-naxiom P: Prop.
+naxiom NP: Prop.
-alias id "P" = "cic:/matita/tests/ng_commands/P.decl".
+ndefinition Q: Prop ≝ NP.
-ndefinition Q: Prop ≝ P.
+include "nat/nat.ma".
nlet rec nzero (n:nat) : nat ≝
match n with
[ O ⇒ O
| S m ⇒ nzero m].
-alias id "nzero" = "cic:/matita/tests/ng_commands/nzero.fix(0,0,0)".
-
ntheorem nzero_ok: nzero (S (S O)) = O.
napply (refl_eq ? O);
nqed.
-(*
-ninductive nnat: Type ≝
- nO: nnat
- | nS: nnat → nnat. *)
\ No newline at end of file
+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}.