helm/software/matita/contribs/RELATIONAL-ARITHMETICS/nat_fwd.ma

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