matita/contribs/RELATIONAL-ARITHMETICS/nat_fwd.ma

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  14
  15 set "baseuri" "cic:/matita/RELATIONAL-ARITHMETICS/nat_fwd".
  16
  17 include "library/logic/equality.ma".
  18 include "nat_defs.ma".
  19
  20 theorem eq_gen_O_S: \forall (P:Prop). \forall m2. O = S m2 \to P.
  21  intros. discriminate H.
  22 qed.
  23
  24 theorem eq_gen_S_O: \forall (P:Prop). \forall m1. S m1 = O \to P.
  25  intros. discriminate H.
  26 qed.
  27
  28 theorem eq_gen_S_S: \forall m1,m2. S m1 = S m2 \to m1 = m2.
  29  intros. injection H. assumption.
  30 qed.