helm/software/matita/tests/tinycals.ma

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  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/tests/tinycals".
  16
  17 theorem prova:
  18   \forall A,B,C:Prop.
  19   \forall H:A \to A \to C \to A \to A \to B.A \to C \to B.
  20 intros.
  21 apply H;
  22   [assumption
  23   |3,5:
  24    [ exact H2;
  25    | exact H1 ]
  26   |4:assumption
  27   |*:assumption
  28   ]
  29 qed.
  30
  31 theorem prova1:
  32   \forall A,B:Prop.
  33   \forall H:A \to A \to A \to A \to A \to B.A \to B.
  34 intros.
  35 apply H;
  36   [*:assumption]
  37 qed.
  38
  39 include "logic/connectives.ma".
  40
  41 theorem prova2:
  42   \forall A,B:Prop.
  43   \forall H:A \to A \to A \to (A \land A) \to A \to B.A \to B.
  44 intros.
  45 apply H;
  46   [2:assumption
  47   |4:split.assumption
  48   |3,5:assumption
  49   |*:assumption
  50   ]
  51 assumption.
  52 qed.
  53