helm/software/matita/contribs/LAMBDA-TYPES/Unified/SUB/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/SUB/Lift/defs".
  16
  17 (* LIFT RELATION
  18    - Usage: invoke with positive polarity
  19 *)
  20
  21 include "SUB/Switch/defs.ma".
  22 include "SUB/Inc/defs.ma".
  23
  24 inductive Lift: Bool \to Nat \to Nat \to Term \to Term \to Prop \def
  25    | lift_sort   : \forall l,q,i,h.
  26                    Lift q l i (leaf (sort h)) (leaf (sort h))
  27    | lift_skip   : \forall l,i,j.
  28                    Lift false l i (leaf (lref j)) (leaf (lref j))
  29    | lift_lref_lt: \forall l,i,j. j < i \to
  30                    Lift true l i (leaf (lref j)) (leaf (lref j))
  31    | lift_lref_ge: \forall l,i,j1. i <= j1 \to
  32                    \forall j2. (j1 + l == j2) \to
  33                    Lift true l i (leaf (lref j1)) (leaf (lref j2))
  34    | lift_head   : \forall l,qt,qu,z. Switch qt z qu \to
  35                    \forall iu,it. Inc qt iu z it \to
  36                    \forall u1,u2. Lift qu l iu u1 u2 \to
  37                    \forall t1,t2. Lift qt l it t1 t2 \to
  38                    Lift qt l iu (head z u1 t1) (head z u2 t2)
  39 .