helm/software/matita/library/logic/connectives2.ma

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  14
  15 include "higher_order_defs/relations.ma".
  16
  17 theorem reflexive_iff: reflexive ? iff.
  18  unfold reflexive;
  19  intro;
  20  split;
  21  intro;
  22  assumption.
  23 qed.
  24
  25 theorem symmetric_iff: symmetric ? iff.
  26  unfold symmetric;
  27  intros;
  28  elim H;
  29  split;
  30  assumption.
  31 qed.
  32
  33 theorem transitive_iff: transitive ? iff.
  34  unfold transitive;
  35  intros;
  36  elim H;
  37  elim H1;
  38  split;
  39  intro;
  40  autobatch.
  41 qed.
  42