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14
15 set "baseuri" "cic:/matita/logic/connectives2".
16
17 include "higher_order_defs/relations.ma".
18
19 theorem reflexive_iff: reflexive ? iff.
20  unfold reflexive;
21  intro;
22  split;
23  intro;
24  assumption.
25 qed.
26
27 theorem symmetric_iff: symmetric ? iff.
28  unfold symmetric;
29  intros;
30  elim H;
31  split;
32  assumption.
33 qed.
34
35 theorem transitive_iff: transitive ? iff.
36  unfold transitive;
37  intros;
38  elim H;
39  elim H1;
40  split;
41  intro;
42  auto.
43 qed.
44