matita/tests/demodulation_matita.ma

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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