-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| A.Asperti, C.Sacerdoti Coen, *)
-(* ||A|| E.Tassi, S.Zacchiroli *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU Lesser General Public License Version 2.1 *)
-(* *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/logic/".
-
-
-inductive True: Prop \def
-I : True.
-
-default "true" cic:/matita/logic/True.ind.
-
-inductive False: Prop \def .
-
-default "false" cic:/matita/logic/False.ind.
-
-definition Not: Prop \to Prop \def
-\lambda A. (A \to False).
-
-theorem absurd : \forall A,C:Prop. A \to Not A \to C.
-intros. elim (H1 H).
-qed.
-
-default "absurd" cic:/matita/logic/absurd.ind.
-
-inductive And (A,B:Prop) : Prop \def
- conj : A \to B \to (And A B).
-
-theorem proj1: \forall A,B:Prop. (And A B) \to A.
-intros. elim H. assumption.
-qed.
-
-theorem proj2: \forall A,B:Prop. (And A B) \to A.
-intros. elim H. assumption.
-qed.
-
-inductive Or (A,B:Prop) : Prop \def
- or_introl : A \to (Or A B)
- | or_intror : B \to (Or A B).
-
-inductive ex (A:Type) (P:A \to Prop) : Prop \def
- ex_intro: \forall x:A. P x \to ex A P.
-
-inductive ex2 (A:Type) (P,Q:A \to Prop) : Prop \def
- ex_intro2: \forall x:A. P x \to Q x \to ex2 A P Q.