helm/software/matita/contribs/LAMBDA-TYPES/Unified-Sub/Lift/props.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 set "baseuri" "cic:/matita/LAMBDA-TYPES/Unified-Sub/Lift/props".
  16
  17 include "Lift/fwd.ma".
  18
  19 alias id "nplus_conf" = "cic:/matita/RELATIONAL/NPlus/props/nplus_conf.con".
  20
  21 axiom pippo: \forall x,y. x < y \to y <= x \to False.
  22
  23 theorem lift_conf: \forall q,h,d,t,x. Lift q h d t x \to
  24                    \forall y. Lift q h d t y \to
  25                    x = y.
  26  intros 6. elim H; clear H q h d t x;
  27  [ lapply linear lift_sort_fwd to H1.
  28    subst. auto
  29  | lapply linear lift_lref_fwd to H1.
  30    decompose; subst;
  31    [ auto | destruct H1 | destruct H ]
  32  | lapply linear lift_lref_fwd to H2.
  33    decompose; subst;
  34    [ destruct H | auto | lapply pippo to H1, H4. decompose ]
  35  | lapply linear lift_lref_fwd to H3.
  36    decompose; subst;
  37    [ destruct H
  38    | lapply linear pippo to H5, H1. decompose
  39    | lapply linear nplus_conf to H2, H4. subst. auto
  40    ]
  41
  42 (*
  43 theorem lift_ct_le: \forall q,h,d,t,y. (Lift q h d t y) \to
  44                     \forall k,e,x. (Lift q k e t x) \to
  45                     \forall z. (Lift q k e y z) \to
  46                     e <= d \to \forall d'. (k + d == d') \to
  47                     (Lift q h d' x z).
  48  intros 6. elim H; clear H q h d t y;
  49  [ lapply linear lift_sort_fwd to H1.
  50    lapply linear lift_sort_fwd to H2.
  51    subst. auto
  52  | lapply linear lift_lref_fwd to H1.
  53    lapply linear lift_lref_fwd to H2.
  54    decompose; subst;
  55    [ auto
  56    | auto
  57    |
  58  *)