helm/software/matita/contribs/LAMBDA-TYPES/Unified/Lift/defs.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/Lift/defs".
  16
  17 (* LIFT RELATION
  18    - Usage: invoke with positive polarity
  19 *)
  20
  21 include "logic/equality.ma".
  22 include "../../RELATIONAL/NPlus/defs.ma".
  23 include "../../RELATIONAL/NLE/defs.ma".
  24 include "../../RELATIONAL/BEq/defs.ma".
  25
  26 include "P/defs.ma".
  27 include "Inc/defs.ma".
  28
  29 inductive Lift (l: Nat): Nat \to Bool \to P \to P \to Prop \def
  30    | lift_sort    : \forall i,a,h. Lift l i a (sort h) (sort h)
  31    | lift_lref_neg: \forall i,j. Lift l i false (lref j) (lref j)
  32    | lift_lref_lt : \forall i,j.
  33                     j < i \to Lift l i true (lref j) (lref j)
  34    | lift_lref_ge : \forall i,j1,j2.
  35                     i <= j1 \to (j1 + l == j2) \to
  36                     Lift l i true (lref j1) (lref j2)
  37    | lift_head    : \forall i,i',a,b,a',z,q1,q2,p1,p2.
  38                     (a * b == a') \to Inc i a' z i' \to
  39                     Lift l i a' q1 q2 \to Lift l i' a p1 p2 \to
  40                     Lift l i a (head b z q1 p1) (head b z q2 p2)
  41 .