matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_fqus.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/s_computation/fqus.ma".
  16 include "basic_2/rt_computation/csx_lsubr.ma".
  17
  18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
  19
  20 (* Properties with extended supclosure **************************************)
  21
  22 lemma csx_fqu_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
  23                     ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
  24 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
  25 [ /3 width=5 by csx_inv_lref_pair, drops_refl/
  26 | /2 width=3 by csx_fwd_pair_sn/
  27 | /2 width=2 by csx_fwd_bind_dx/
  28 | /2 width=4 by csx_fwd_bind_dx_unit/
  29 | /2 width=3 by csx_fwd_flat_dx/
  30 | /4 width=7 by csx_inv_lifts, drops_refl, drops_drop/
  31 ]
  32 qed-.
  33
  34 lemma csx_fquq_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
  35                      ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
  36 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=6 by csx_fqu_conf/
  37 * #HG #HL #HT destruct //
  38 qed-.
  39
  40 lemma csx_fqup_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
  41                      ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
  42 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
  43 /3 width=6 by csx_fqu_conf/
  44 qed-.
  45
  46 lemma csx_fqus_conf: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
  47                      ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
  48 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -H
  49 /3 width=6 by csx_fquq_conf/
  50 qed-.