(* *)
(**************************************************************************)
-include "nat/plus.ma".
+include "ng_pts.ma".
ndefinition thesis0: ∀A:Type.Type ≝ λA. A → A.
ndefinition Q: Prop ≝ NP.
+include "nat/nat.ma".
+
nlet rec nzero (n:nat) : nat ≝
match n with
[ O ⇒ O
napply (refl_eq ? O);
nqed.
-(*
-ninductive nnat: Type ≝
- nO: nnat
- | nS: nnat → nnat.
-*)
-
-(* testare anche i record e le ricorsioni/coricorsioni/(co)induttivi MUTUI *)
-
-(*
-nrecord pair: Type ≝ { l: pair; r: pair }.
-*)
\ 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}.