set "baseuri" "cic:/matita/LOGIC/Track/order".
-include "Track/props.ma".
+include "Insert/fun.ma".
+include "Track/defs.ma".
(* Order properties *********************************************************)
decompose; autobatch depth = 5 width = 4 size = 8
].
qed.
-(*
-theorem track_trans: \forall p,q,A,B. \forall c:Formula.
- Track leaf p (pair A c) \to Track leaf q (pair c B) \to
- \exists r. Track leaf r (pair A B).
- intros 1; elim p names 0; clear p;
- [ intros; clear H1;
- lapply linear track_inv_lref to H; decompose;
- lapply insert_inv_leaf_2 to H; decompose
- | intros;
- lapply linear track_inv_parx to H; subst; autobatch;
- | intros;
- lapply linear track_inv_impw to H1;
- decompose; subst;
- lapply linear H to H4, H2; decompose; autobatch
- | intros 3; elim q; clear q;
- [ clear H H1;
- lapply linear track_inv_lref to H2; decompose;
- lapply insert_inv_leaf_2 to H; decompose
- | lapply linear track_inv_parx to H2; subst; autobatch
- | clear H H1;
- lapply linear track_inv_impr to H2;
- lapply linear track_inv_impw to H3;
- decompose; subst; autobatch
- | clear H H1 H2;
- lapply linear track_inv_impr to H3;
- decompose; subst
- | clear H2 H3;
- lapply linear track_inv_impr to H4;
- lapply linear track_inv_impi to H5;
- decompose; subst;
- lapply linear H to H5, H8; decompose;
-
-
- lapply linear insert_inv_leaf_1 to H4; decompose; subst;
- apply ex_intro; [| ]
-
- autobatch depth = 100 width = 40 size = 100
- ]
- | intros 3; elim q; clear q;
- [ clear H H1;
- lapply linear track_inv_lref to H2; decompose;
- lapply insert_inv_leaf_2 to H; decompose
- | clear H;
- lapply linear track_inv_parx to H2;
- subst; autobatch
- | clear H H1;
- lapply linear track_inv_impe to H2;
- lapply linear track_inv_impw to H3;
- decompose; subst; autobatch
- | clear H H1 H2;
- lapply linear track_inv_impi to H3; decompose; subst
- | clear H H1;
- lapply linear track_inv_impe to H2;
- lapply linear track_inv_impe to H3;
- decompose; subst;
- lapply linear track_inv_lleaf_impl to H5; decompose; subst;
- [ clear H4 H6;
- lapply linear insert_inv_leaf_1 to H3; decompose; subst;
- lapply linear insert_inv_abst_2 to H2; decompose; subst
- | lapply insert_conf to H3, H4; clear H4; decompose;
- lapply linear track_weak to H6, H4; decompose;
- lapply linear track_comp to H2, H, H1; decompose; autobatch
- ]
- ]
- ].
-qed.
-(*
- | lapply linear track_inv_impi to H4;
- lapply linear track_inv_impe to H5;
- decompose; subst;
- destruct H4; destruct H5; clear H4 H5; subst;
- unfold linj in Hcut; unfold rinj in Hcut3; destruct Hcut; destruct Hcut3; clear Hcut Hcut3; subst;
- destruct Hcut2; clear Hcut2; subst;
-*)
-*)
+
+theorem track_trans: \forall P,p,q,A,B. \forall c:Formula.
+ Track P p (pair A c) \to Track P q (pair c B) \to
+ \exists r. Track P r (pair A B).
+ intros; autobatch.
+qed.