matita/matita/contribs/lambdadelta/basic_2/static/lsuba_ldrop.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 "basic_2/static/lsuba.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
  18
  19 (* Properties concerning basic local environment slicing ********************)
  20
  21 (* Note: the constant 0 cannot be generalized *)
  22 lemma lsuba_ldrop_O1_conf: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
  23                            ∃∃K2. G ⊢ K1 ⁝⫃ K2 & ⇩[s, 0, e] L2 ≡ K2.
  24 #G #L1 #L2 #H elim H -L1 -L2
  25 [ /2 width=3/
  26 | #I #L1 #L2 #V #_ #IHL12 #K1 #s #e #H
  27   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
  28   [ destruct
  29     elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
  30     <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, ldrop_pair, ex2_intro/
  31   | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
  32   ]
  33 | #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K1 #s #e #H
  34   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
  35   [ destruct
  36     elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
  37     <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, ldrop_pair, ex2_intro/
  38   | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
  39   ]
  40 ]
  41 qed-.
  42
  43 (* Note: the constant 0 cannot be generalized *)
  44 lemma lsuba_ldrop_O1_trans: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
  45                             ∃∃K1. G ⊢ K1 ⁝⫃ K2 & ⇩[s, 0, e] L1 ≡ K1.
  46 #G #L1 #L2 #H elim H -L1 -L2
  47 [ /2 width=3/
  48 | #I #L1 #L2 #V #_ #IHL12 #K2 #s #e #H
  49   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
  50   [ destruct
  51     elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
  52     <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, ldrop_pair, ex2_intro/
  53   | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
  54   ]
  55 | #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K2 #s #e #H
  56   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
  57   [ destruct
  58     elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
  59     <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, ldrop_pair, ex2_intro/
  60   | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
  61   ]
  62 ]
  63 qed-.