matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_drops.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 include "static_2/relocation/drops.ma".
  16 include "basic_2/dynamic/lsubv.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
  19
  20 (* Properties with generic slicing for local environments *******************)
  21
  22 (* Note: the premise 𝐔❪f❫ cannot be removed *)
  23 (* Basic_2A1: includes: lsubsv_drop_O1_conf *)
  24 lemma lsubv_drops_conf_isuni (h) (a) (G):
  25       ∀L1,L2. G ⊢ L1 ⫃![h,a] L2 →
  26       ∀b,f,K1. 𝐔❪f❫ → ⇩*[b,f] L1 ≘ K1 →
  27       ∃∃K2. G ⊢ K1 ⫃![h,a] K2 & ⇩*[b,f] L2 ≘ K2.
  28 #h #a #G #L1 #L2 #H elim H -L1 -L2
  29 [ /2 width=3 by ex2_intro/
  30 | #I #L1 #L2 #HL12 #IH #b #f #K1 #Hf #H
  31   elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
  32   [ #Hf #H destruct -IH
  33     /3 width=3 by lsubv_bind, drops_refl, ex2_intro/
  34   | #g #Hg #HLK1 #H destruct -HL12
  35     elim (IH … Hg HLK1) -L1 -Hg /3 width=3 by drops_drop, ex2_intro/
  36   ]
  37 | #L1 #L2 #W #V #HVW #HL12 #IH #b #f #K1 #Hf #H
  38   elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
  39   [ #Hf #H destruct -IH
  40     /3 width=3 by drops_refl, lsubv_beta, ex2_intro/
  41   | #g #Hg #HLK1 #H destruct -HL12
  42     elim (IH … Hg HLK1) -L1 -Hg /3 width=3 by drops_drop, ex2_intro/
  43   ]
  44 ]
  45 qed-.
  46
  47 (* Note: the premise 𝐔❪f❫ cannot be removed *)
  48 (* Basic_2A1: includes: lsubsv_drop_O1_trans *)
  49 lemma lsubv_drops_trans_isuni (h) (a) (G):
  50       ∀L1,L2. G ⊢ L1 ⫃![h,a] L2 →
  51       ∀b,f,K2. 𝐔❪f❫ → ⇩*[b,f] L2 ≘ K2 →
  52       ∃∃K1. G ⊢ K1 ⫃![h,a] K2 & ⇩*[b,f] L1 ≘ K1.
  53 #h #a #G #L1 #L2 #H elim H -L1 -L2
  54 [ /2 width=3 by ex2_intro/
  55 | #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H
  56   elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
  57   [ #Hf #H destruct -IH
  58     /3 width=3 by lsubv_bind, drops_refl, ex2_intro/
  59   | #g #Hg #HLK2 #H destruct -HL12
  60     elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
  61   ]
  62 | #L1 #L2 #W #V #HWV #HL12 #IH #b #f #K2 #Hf #H
  63   elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
  64   [ #Hf #H destruct -IH
  65     /3 width=3 by drops_refl, lsubv_beta, ex2_intro/
  66   | #g #Hg #HLK2 #H destruct -HL12
  67     elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
  68   ]
  69 ]
  70 qed-.