matita/matita/contribs/lambdadelta/basic_2/static/lsuba_drops.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  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/notation/relations/lrsubeqa_3.ma".
  16 include "basic_2/static/lsubr.ma".
  17 include "basic_2/static/aaa.ma".
  18
  19 (* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
  20
  21 (* Basic properties *********************************************************)
  22
  23 (* Note: the constant 0 cannot be generalized *)
  24 lemma lsuba_drop_O1_conf: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀K1,c,k. ⬇[c, 0, k] L1 ≡ K1 →
  25                           ∃∃K2. G ⊢ K1 ⫃⁝ K2 & ⬇[c, 0, k] L2 ≡ K2.
  26 #G #L1 #L2 #H elim H -L1 -L2
  27 [ /2 width=3 by ex2_intro/
  28 | #I #L1 #L2 #V #_ #IHL12 #K1 #c #k #H
  29   elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK1
  30   [ destruct
  31     elim (IHL12 L1 c 0) -IHL12 // #X #HL12 #H
  32     <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, drop_pair, ex2_intro/
  33   | elim (IHL12 … HLK1) -L1 /3 width=3 by drop_drop_lt, ex2_intro/
  34   ]
  35 | #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K1 #c #k #H
  36   elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK1
  37   [ destruct
  38     elim (IHL12 L1 c 0) -IHL12 // #X #HL12 #H
  39     <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_beta, drop_pair, ex2_intro/
  40   | elim (IHL12 … HLK1) -L1 /3 width=3 by drop_drop_lt, ex2_intro/
  41   ]
  42 ]
  43 qed-.
  44
  45 (* Note: the constant 0 cannot be generalized *)
  46 lemma lsuba_drop_O1_trans: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀K2,c,k. ⬇[c, 0, k] L2 ≡ K2 →
  47                            ∃∃K1. G ⊢ K1 ⫃⁝ K2 & ⬇[c, 0, k] L1 ≡ K1.
  48 #G #L1 #L2 #H elim H -L1 -L2
  49 [ /2 width=3 by ex2_intro/
  50 | #I #L1 #L2 #V #_ #IHL12 #K2 #c #k #H
  51   elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK2
  52   [ destruct
  53     elim (IHL12 L2 c 0) -IHL12 // #X #HL12 #H
  54     <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, drop_pair, ex2_intro/
  55   | elim (IHL12 … HLK2) -L2 /3 width=3 by drop_drop_lt, ex2_intro/
  56   ]
  57 | #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K2 #c #k #H
  58   elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK2
  59   [ destruct
  60     elim (IHL12 L2 c 0) -IHL12 // #X #HL12 #H
  61     <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_beta, drop_pair, ex2_intro/
  62   | elim (IHL12 … HLK2) -L2 /3 width=3 by drop_drop_lt, ex2_intro/
  63   ]
  64 ]
  65 qed-.