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[helm.git] / matita / contribs / LOGIC / Insert / props.ma

diff --git a/matita/contribs/LOGIC/Insert/props.ma b/matita/contribs/LOGIC/Insert/props.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+(*
+*)
+
+include "Insert/fun.ma".
+(*
+theorem insert_conf: \forall P,Q1,S1,i1. Insert S1 i1 P Q1 \to 
+                     \forall Q2,S2,i2. Insert S2 i2 P Q2 \to
+                     \exists Q,j1,j2. 
+                     Insert S2 j2 Q1 Q \land Insert S1 j1 Q2 Q.
+ intros 5. elim H; clear H i1 P Q1;
+ [ elim H1; clear H1 i2 c Q2; decompose; autobatch depth = 7 size = 8
+ | lapply linear insert_inv_abst_1 to H3. decompose; destruct;
+   [ autobatch depth = 7 size = 8
+   | lapply linear H2 to H4. decompose. destruct. autobatch depth = 6 size = 8
+   ]
+ ].
+qed. 
+
+theorem insert_trans: \forall P1,Q1,S1,i1. Insert S1 i1 P1 Q1 \to 
+                      \forall Q2,S2,i2. Insert S2 i2 Q1 Q2 \to
+                      \exists P2,j1,j2. 
+                      Insert S2 j2 P1 P2 \land Insert S1 j1 P2 Q2.
+ intros 5. elim H; clear H i1 P1 Q1;
+ [ lapply linear insert_inv_abst_1 to H1. decompose; destruct; autobatch depth = 6 size = 7
+ | lapply linear insert_inv_abst_1 to H3. decompose; destruct;
+   [ clear H2. autobatch depth = 7 size = 8
+   | lapply linear H2 to H4. decompose. destruct. autobatch depth = 6 size = 8
+   ]
+ ].
+qed.
+
+theorem insert_conf_rev: \forall P1,Q,S1,i1. Insert S1 i1 P1 Q \to 
+                         \forall P2,S2,i2. Insert S2 i2 P2 Q \to
+                         (i1 = i2 \land P1 = P2) \lor 
+                         \exists Q1,Q2,j1,j2. 
+                         Insert S2 j2 Q2 P1 \land Insert S1 j1 Q1 P2.
+ intros 5; elim H; clear H i1 P1 Q;
+ [ inversion H1; clear H1; intros; destruct; autobatch depth = 7 size = 8
+ | inversion H3; clear H3; intros; destruct;
+   [ autobatch depth = 7 size = 8
+   | clear H3; lapply linear H2 to H; decompose; destruct;
+     autobatch depth = 8 size = 10
+   ]
+ ].
+qed.
+
+theorem insert_conf_rev_full: \forall P1,Q,S1,i1. Insert S1 i1 P1 Q \to 
+                              \forall P2,S2,i2. Insert S2 i2 P2 Q \to
+                              (S1 = S2 \land i1 = i2 \land P1 = P2) \lor 
+                              \exists Q1,Q2,j1,j2. 
+                              Insert S2 j2 Q2 P1 \land Insert S1 j1 Q1 P2.
+ intros; lapply insert_conf_rev to H, H1; decompose; destruct;
+ [ lapply linear insert_inj to H, H1; destruct; autobatch depth = 4
+ | autobatch depth = 7 size = 8
+ ].
+qed.
+*)