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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 set "baseuri" "cic:/matita/LOGIC/Track/order".
17 include "Insert/fun.ma".
18 include "Track/defs.ma".
20 (* Order properties *********************************************************)
22 theorem track_refl: \forall P. \forall c:Formula. \exists r.
24 intros; elim c; clear c;
26 | lapply (insert_total (pair f f1) zero P); [2:autobatch];
27 decompose; autobatch depth = 5 width = 4 size = 8
31 theorem track_trans: \forall P,p,q,A,B. \forall c:Formula.
32 Track P p (pair A c) \to Track P q (pair c B) \to
33 \exists r. Track P r (pair A B).