matita/contribs/LOGIC/Insert/inv.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15
  16
  17 (*
  18 *)
  19
  20 include "Insert/defs.ma".
  21 (*
  22 theorem insert_inv_zero: \forall S,P,Q. Insert S zero P Q \to Q = abst P S.
  23  intros; inversion H; clear H; intros; destruct; autobatch.
  24 qed.
  25
  26 theorem insert_inv_succ: \forall S,Q1,Q2,i. Insert S (succ i) Q1 Q2 \to
  27                          \exists P1,P2,R. Insert S i P1 P2 \land
  28                                           Q1 = abst P1 R \land Q2 = abst P2 R.
  29  intros; inversion H; clear H; intros; destruct; autobatch depth = 6 size = 8.
  30 qed.
  31
  32 theorem insert_inv_leaf_1: \forall Q,S,i. Insert S i leaf Q \to
  33                            i = zero \land Q = S.
  34  intros. inversion H; clear H; intros; destruct. autobatch.
  35 qed.
  36
  37 theorem insert_inv_abst_1: \forall P,Q,R,S,i. Insert S i (abst P R) Q \to
  38                            (i = zero \land Q = (abst (abst P R) S)) \lor
  39                            \exists n, c1.
  40                            i = succ n \land Q = abst c1 R \land
  41                            Insert S n P c1.
  42  intros. inversion H; clear H; intros; destruct; autobatch depth = 6 size =  8.
  43 qed.
  44
  45 theorem insert_inv_leaf_2: \forall P,S,i. Insert S i P leaf \to False.
  46  intros. inversion H; clear H; intros; destruct.
  47 qed.
  48
  49 theorem insert_inv_abst_2: \forall P,i. \forall R,S:Sequent.
  50                            Insert S i P R \to
  51                            i = zero \land P = leaf \land R = S.
  52  intros. inversion H; clear H; intros; destruct;
  53  [ autobatch
  54  | clear H1. lapply linear insert_inv_leaf_2 to H. decompose
  55  ].
  56 qed.
  57 *)