(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/LOGIC/Insert/inv".
+
(*
*)
include "Insert/defs.ma".
-
+(*
theorem insert_inv_zero: \forall S,P,Q. Insert S zero P Q \to Q = abst P S.
- intros; inversion H; clear H; intros; subst; autobatch.
+ intros; inversion H; clear H; intros; destruct; autobatch.
qed.
theorem insert_inv_succ: \forall S,Q1,Q2,i. Insert S (succ i) Q1 Q2 \to
\exists P1,P2,R. Insert S i P1 P2 \land
Q1 = abst P1 R \land Q2 = abst P2 R.
- intros; inversion H; clear H; intros; subst; autobatch depth = 6 size = 8.
+ intros; inversion H; clear H; intros; destruct; autobatch depth = 6 size = 8.
qed.
theorem insert_inv_leaf_1: \forall Q,S,i. Insert S i leaf Q \to
i = zero \land Q = S.
- intros. inversion H; clear H; intros; subst. autobatch.
+ intros. inversion H; clear H; intros; destruct. autobatch.
qed.
theorem insert_inv_abst_1: \forall P,Q,R,S,i. Insert S i (abst P R) Q \to
\exists n, c1.
i = succ n \land Q = abst c1 R \land
Insert S n P c1.
- intros. inversion H; clear H; intros; subst; autobatch depth = 6 size = 8.
+ intros. inversion H; clear H; intros; destruct; autobatch depth = 6 size = 8.
qed.
theorem insert_inv_leaf_2: \forall P,S,i. Insert S i P leaf \to False.
- intros. inversion H; clear H; intros; subst.
+ intros. inversion H; clear H; intros; destruct.
qed.
theorem insert_inv_abst_2: \forall P,i. \forall R,S:Sequent.
Insert S i P R \to
i = zero \land P = leaf \land R = S.
- intros. inversion H; clear H; intros; subst;
+ intros. inversion H; clear H; intros; destruct;
[ autobatch
| clear H1. lapply linear insert_inv_leaf_2 to H. decompose
].
qed.
+*)