(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/LOGIC/Insert/props".
+
(*
*)
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; subst;
+ | lapply linear insert_inv_abst_1 to H3. decompose; destruct;
[ autobatch depth = 7 size = 8
- | lapply linear H2 to H4. decompose. subst. autobatch depth = 6 size = 8
+ | lapply linear H2 to H4. decompose. destruct. autobatch depth = 6 size = 8
]
].
qed.
\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; subst; autobatch depth = 6 size = 7
- | lapply linear insert_inv_abst_1 to H3. decompose; subst;
+ [ 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. subst. autobatch depth = 6 size = 8
+ | lapply linear H2 to H4. decompose. destruct. autobatch depth = 6 size = 8
]
].
qed.
\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; subst; autobatch depth = 7 size = 8
- | inversion H3; clear H3; intros; subst;
+ [ 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; subst;
+ | clear H3; lapply linear H2 to H; decompose; destruct;
autobatch depth = 8 size = 10
]
].
(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; subst;
- [ lapply linear insert_inj to H, H1; subst; autobatch depth = 4
+ 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.
+*)