helm/software/matita/tests/demodulation_matita.ma

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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