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fixed some notational collisions
[helm.git] / helm / software / matita / library / logic / coimplication.ma
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14
15 include "logic/connectives.ma".
16
17 definition Iff : Prop \to Prop \to Prop \def
18    \lambda A,B. (A \to B) \land (B \to A).
19    
20 interpretation "logical iff" 'iff x y = (Iff x y).
21
22 theorem iff_intro: \forall A,B. (A \to B) \to (B \to A) \to (A \liff B).
23  unfold Iff. intros. split; intros; autobatch.
24 qed.
25
26 theorem iff_refl: \forall A. A \liff A.
27  intros. apply iff_intro; intros; autobatch.
28 qed.
29
30 theorem iff_sym: \forall A,B. A \liff B \to B \liff A.
31  intros. elim H. apply iff_intro[assumption|assumption]
32 qed.
33
34 theorem iff_trans: \forall A,B,C. A \liff B \to B \liff C \to A \liff C.
35  intros. elim H. elim H1. apply iff_intro;intros;autobatch.
36 qed.