matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_lift.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   9 (*      \   /                                                             *)
  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_2/unfold/lsstas_lift.ma".
  16 include "basic_2/reduction/fpb_lift.ma".
  17 include "basic_2/reduction/fpbc_lift.ma".
  18 include "basic_2/computation/fpbg.ma".
  19
  20 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
  21
  22 (* Advanced properties ******************************************************)
  23
  24 lemma lsstas_fpbg: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 → (T1 = T2 → ⊥) →
  25                    ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
  26 #h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2
  27 [ #H elim H //
  28 | #l2 #T #T2 #HT1 #HT2 #IHT1 #HT12 #l1 #Hl21
  29   elim (term_eq_dec T1 T) #H destruct [ -IHT1 |]
  30   [ elim (le_inv_plus_l … Hl21) -Hl21 #_ #Hl1
  31     >(plus_minus_m_m … Hl1) -Hl1 /3 width=5 by ssta_fpbc, fpbg_inj/
  32   | #Hl1 >commutative_plus in Hl21; #Hl21
  33     elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
  34     lapply (lsstas_da_conf … HT1 … Hl1) -HT1
  35     >(plus_minus_m_m … Hl12) -Hl12
  36     /4 width=5 by ssta_fpb, fpbg_strap1/
  37   ]
  38 ]
  39 qed.