helm/software/matita/tests/applys.ma

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  14
  15
  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 (* se non trova subito sym_times poi si perde! *)
  34 (* alternativamente si puo' abilitare la are_convertible nella
  35    is_identity, ma poi va peggio nel resto (conv lunghe) *)
  36 letin www \def sym_times.
  37 clearbody www.
  38 applyS (witness ? ? ? (refl_eq ? ?)).
  39 qed.