1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| A.Asperti, C.Sacerdoti Coen, *)
8 (* ||A|| E.Tassi, S.Zacchiroli *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU Lesser General Public License Version 2.1 *)
13 (**************************************************************************)
15 set "baseuri" "cic:/matita/datatypes/constructors/".
16 include "logic/equality.ma".
18 inductive void : Set \def.
20 inductive Prod (A,B:Set) : Set \def
21 pair : A \to B \to Prod A B.
23 definition fst \def \lambda A,B:Set.\lambda p: Prod A B.
25 [(pair a b) \Rightarrow a].
27 definition snd \def \lambda A,B:Set.\lambda p: Prod A B.
29 [(pair a b) \Rightarrow b].
31 theorem eq_pair_fst_snd: \forall A,B:Set.\forall p: Prod A B.
32 p = pair A B (fst A B p) (snd A B p).
33 intros.elim p.simplify.reflexivity.
36 inductive Sum (A,B:Set) : Set \def
38 | inr : B \to Sum A B.