matita/matita/contribs/lambdadelta/basic_2A/multiple/drops_drop.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2A/substitution/drop_drop.ma".
  16 include "basic_2A/multiple/drops.ma".
  17
  18 (* ITERATED LOCAL ENVIRONMENT SLICING ***************************************)
  19
  20 (* Properties concerning basic local environment slicing ********************)
  21
  22 lemma drops_drop_trans: ∀L1,L,cs. ⬇*[Ⓕ, cs] L1 ≡ L → ∀L2,i. ⬇[i] L ≡ L2 →
  23                         ∃∃L0,cs0,i0. ⬇[i0] L1 ≡ L0 & ⬇*[Ⓕ, cs0] L0 ≡ L2 &
  24                                       @⦃i, cs⦄ ≡ i0 & cs ▭ i ≡ cs0.
  25 #L1 #L #cs #H elim H -L1 -L -cs
  26 [ /2 width=7 by drops_nil, minuss_nil, at_nil, ex4_3_intro/
  27 | #L1 #L0 #L #cs #l #m #_ #HL0 #IHL0 #L2 #i #HL2
  28   elim (lt_or_ge i l) #Hil
  29   [ elim (drop_trans_le … HL0 … HL2) -L /2 width=2 by lt_to_le/
  30     #L #HL0 #HL2 elim (IHL0 … HL0) -L0 /3 width=7 by drops_cons, minuss_lt, at_lt, ex4_3_intro/
  31   | lapply (drop_trans_ge … HL0 … HL2 ?) -L // #HL02
  32     elim (IHL0 … HL02) -L0 /3 width=7 by minuss_ge, at_ge, ex4_3_intro/
  33   ]
  34 ]
  35 qed-.