matita/matita/contribs/RELATIONAL/ZEq/setoid.ma

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  14
  15
  16
  17 include "NPlus/fun.ma".
  18 include "ZEq/defs.ma".
  19
  20 theorem zeq_refl: ∀z. z ≈ z.
  21  intros; elim z. clear z.
  22  lapply (nplus_total a b); decompose;
  23  autobatch.
  24 qed.
  25
  26 theorem zeq_sym: ∀z1,z2. z1 ≈ z2 → z2 ≈ z1.
  27  intros; elim H; clear H z1 z2; autobatch.
  28 qed.
  29 (*
  30 theorem zeq_trans: \forall z1,z2. z1 = z2 \to
  31                    \forall z3. z2 = z3 \to z1 = z3.
  32  intros 3. elim H. clear H z1 z2.
  33  inversion H3. clear H3. intros. destruct.
  34  lapply (nplus_total n5 n6). decompose.
  35  lapply (nplus_total n4 n9). decompose.
  36  apply zeq.
  37 *)