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14
15
16
17 include "nat/minus.ma".
18
19 theorem p2: \forall x,y:nat. x+x = (S(S O))*x.
20 intros.
21 demodulate by times_n_Sm times_n_O sym_times plus_n_O.
22 qed.
23
24 theorem p4: \forall x:nat. (x+(S O))*(x-(S O))=x*x - (S O).
25 intro.
26 apply (nat_case x)
27 [simplify.reflexivity
28 |intro.demodulate.reflexivity]
29 qed.
30
31 theorem p5: \forall x,y:nat. (x+y)*(x+y) = x*x + (S(S O))*(x*y) + (y*y).
32 intros.demodulate.reflexivity.
33 qed.
34