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restored the good factorization file
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3 (*      ||M||                                                             *)
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14
15 set "baseuri" "cic:/matita/demodulation_matita/".
16
17 include "nat/minus.ma".
18
19 theorem p2: \forall x,y:nat. x+x = (S(S O))*x.
20 intros.demodulate.reflexivity.
21 qed.
22
23 theorem p4: \forall x:nat. (x+(S O))*(x-(S O))=x*x - (S O).
24 intro.
25 apply (nat_case x)
26 [simplify.reflexivity
27 |intro.demodulate.reflexivity]
28 qed.
29
30 theorem p5: \forall x,y:nat. (x+y)*(x+y) = x*x + (S(S O))*(x*y) + (y*y).
31 intros.demodulate.reflexivity.
32 qed.
33