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

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  14
  15 include "basic_2/computation/lsx_csx.ma".
  16 include "basic_2/computation/fsb_alt.ma".
  17
  18 axiom fqup_lpxs_trans_nlleq: ∀h,g,G1,G2,K1,K2,T1,T2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ →
  19                              ∀L2. ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 → (K2 ⋕[T2, 0] L2 →⊥) →
  20                              ∃∃L1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 &
  21                                    K1 ⋕[T1, 0] L1 → ⊥ & ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄.
  22
  23 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
  24
  25 (* Advanced propreties on context-senstive extended bormalizing terms *******)
  26
  27 lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
  28 #h #g #G1 #L1 #T1 #H @(csx_ind_alt … H) -T1
  29 #T1 #HT1 @(csx_ind_lsx … (yinj 0) … HT1) -L1
  30 #L1 @(fqup_wf_ind … G1 L1 T1) -G1 -L1 -T1
  31 #G1 #L1 #T1 #IHu #H1 #IHl #IHc @fsb_intro
  32 #G2 #L2 #T2 * -G2 -L2 -T2
  33 [ #G2 #L2 #T2 #H12 @IHu -IHu // /2 width=5 by csx_fqup_conf/ -H1 [| -IHl ]
  34   [ #L0 #HL20 #HnL20 #_ elim (fqup_lpxs_trans_nlleq … H12 … HL20 HnL20) -L2
  35     /6 width=5 by fsb_fpbs_trans, lpxs_fpbs, fqup_fpbs, lpxs_cpxs_trans/
  36   | #T0 #HT20 #HnT20 elim (fqup_cpxs_trans_neq … H12 … HT20 HnT20) -T2
  37     /4 width=5 by fsb_fpbs_trans, fqup_fpbs/
  38   ]
  39 | -H1 -IHu -IHl /3 width=1 by/
  40 | -H1 -IHu /5 width=5 by fsb_fpbs_trans, lpxs_fpbs, lpxs_cpxs_trans/
  41 ]
  42 qed.
  43
  44 (* Advanced eliminators *****************************************************)
  45
  46 lemma csx_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
  47                     (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  48                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  49                                 R G1 L1 T1
  50                     ) →
  51                     ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
  52 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
  53
  54 lemma csx_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
  55                     (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
  56                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  57                                 R G1 L1 T1
  58                     ) →
  59                     ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
  60 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.