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3 (*      ||M||                                                             *)
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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.