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[helm.git] / matita / tests / tinycals.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+theorem prova: 
+  \forall A,B,C:Prop.
+  \forall H:A \to A \to C \to A \to A \to B.A \to C \to B.
+intros.
+apply H;
+  [assumption 
+  |3,5:
+   [ exact H2;
+   | exact H1 ]
+  |4:assumption
+  |*:assumption
+  ]
+qed.
+
+theorem prova1: 
+  \forall A,B:Prop.
+  \forall H:A \to A \to A \to A \to A \to B.A \to B.
+intros.
+apply H;
+  [*:assumption]
+qed. 
+
+include "logic/connectives.ma".
+
+theorem prova2: 
+  \forall A,B:Prop.
+  \forall H:A \to A \to A \to (A \land A) \to A \to B.A \to B.
+intros.
+apply H;
+  [2:assumption
+  |4:split.assumption
+  |3,5:assumption
+  |*:assumption
+  ]
+assumption.
+qed. 
+