matita/tests/applys.ma

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/test/applys".
  16
  17 include "nat/div_and_mod.ma".
  18 include "nat/factorial.ma".
  19 include "nat/primes.ma".
  20
  21 theorem prova : \forall n. (n+O)*(S O) = n.
  22 intro.
  23 applyS times_n_SO.
  24 qed.
  25
  26 lemma foo: ∀n.(S n)! = (S n) * n!.
  27 intro; reflexivity.
  28 qed.
  29
  30 theorem prova2 :
  31  \forall n. S n \divides (S n)!.
  32 intros.
  33 applyS (witness ? ? ? (refl_eq ? ?)).
  34 qed.