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

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   5 (*      ||T||                                                             *)
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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/computation/fpbs_ext.ma".
  16 include "basic_2/computation/csx_fpbs.ma".
  17 include "basic_2/computation/lsx_csx.ma".
  18 include "basic_2/computation/fsb_alt.ma".
  19
  20 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
  21
  22 (* Advanced propreties on context-senstive extended bormalizing terms *******)
  23
  24 lemma csx_fsb_fpbs: ∀h,g,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  25                     ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⦥[h, g] T2.
  26 #h #g #G1 #L1 #T1 #H @(csx_ind_alt … H) -T1
  27 #T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind … G2 L2 T2) -G2 -L2 -T2
  28 #G0 #L0 #T0 #IHu #H10 lapply (csx_fpbs_conf … H10) // -HT1
  29 #HT0 generalize in match IHu; -IHu generalize in match H10; -H10
  30 @(lsx_ind_alt … (csx_lsx … HT0 0)) -L0
  31 #L0 #_ #IHl #H10 #IHu @fsb_intro
  32 #G2 #L2 #T2 * -G2 -L2 -T2 [ -IHl -IHc | -IHu -IHl |  ]
  33 [ /3 width=5 by fpbs_fqup_trans/
  34 | #T2 #HT02 #HnT02 elim (fpbs_cpxs_trans_neq … H10 … HT02 HnT02) -T0
  35   /3 width=4 by/
  36 | #L2 #HL02 #HnL02 @(IHl … HL02 HnL02) -IHl -HnL02 [ -IHu -IHc | ]
  37   [ /2 width=3 by fpbs_lpxs_trans/
  38   | #G3 #L3 #T3 #H03 #_ elim (lpxs_fqup_trans … H03 … HL02) -L2
  39     #L4 #T4 elim (eq_term_dec T0 T4) [ -IHc | -IHu ]
  40     [ #H destruct /4 width=5 by fsb_fpbs_trans, lpxs_fpbs, fpbs_fqup_trans/
  41     | #HnT04 #HT04 #H04 elim (fpbs_cpxs_trans_neq … H10 … HT04 HnT04) -T0
  42       /4 width=8 by fpbs_fqup_trans, fpbs_lpxs_trans/
  43     ]
  44   ]
  45 ]
  46 qed.
  47
  48 lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
  49 /2 width=5 by csx_fsb_fpbs/ qed.
  50
  51 (* Advanced eliminators *****************************************************)
  52
  53 lemma csx_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
  54                     (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  55                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  56                                 R G1 L1 T1
  57                     ) →
  58                     ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
  59 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
  60
  61 lemma csx_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
  62                     (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  63                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  64                                 R G1 L1 T1
  65                     ) →
  66                     ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
  67 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.