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 "Term/defs.ma".
  22
  23 inductive Lift: Bool \to Nat \to Nat \to Term \to Term \to Prop \def
  24    | lift_sort   : \forall l,q,i,h.
  25                    Lift q l i (leaf (sort h)) (leaf (sort h))
  26    | lift_lref   : \forall l,i,j.
  27                    Lift false l i (leaf (lref j)) (leaf (lref j))
  28    | lift_lref_lt: \forall l,i,j. j < i \to
  29                    Lift true l i (leaf (lref j)) (leaf (lref j))
  30    | lift_lref_ge: \forall l,i,j1. i <= j1 \to
  31                    \forall j2. (j1 + l == j2) \to
  32                    Lift true l i (leaf (lref j1)) (leaf (lref j2))
  33    | lift_bind   : \forall l,i,u1,u2. Lift true l i u1 u2 \to
  34                    \forall q,t1,t2. Lift q l (succ i) t1 t2 \to
  35                    \forall r.
  36                    Lift q l i (head q (bind r) u1 t1) (head q (bind r) u2 t2)
  37    | lift_flat   : \forall l,i,u1,u2. Lift true l i u1 u2 \to
  38                    \forall q,t1,t2. Lift q l i t1 t2 \to
  39                    \forall r.
  40                    Lift q l i (head q (flat r) u1 t1) (head q (flat r) u2 t2)
  41    | lift_head   : \forall l,q,p. (p = q \to False) \to
  42                    \forall i,u1,u2. Lift false l i u1 u2 \to
  43                    \forall t1,t2. Lift q l i t1 t2 \to
  44                    \forall z.
  45                    Lift q l i (head p z u1 t1) (head p z u2 t2)
  46 .