matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_csx.ma

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   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                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/rt_computation/csx_lsubr.ma".
  16 include "basic_2/rt_computation/csx_cpxs.ma".
  17 include "basic_2/rt_computation/lsubsx_rdsx.ma".
  18
  19 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 (* Basic_2A1: uses: lsx_lref_be_lpxs *)
  24 lemma rdsx_pair_lpxs (h) (o) (G):
  25                      ∀K1,V. ⦃G, K1⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ →
  26                      ∀K2. G ⊢ ⬈*[h, o, V] 𝐒⦃K2⦄ → ⦃G, K1⦄ ⊢ ⬈*[h] K2 →
  27                      ∀I. G ⊢ ⬈*[h, o, #0] 𝐒⦃K2.ⓑ{I}V⦄.
  28 #h #o #G #K1 #V #H
  29 @(csx_ind_cpxs … H) -V #V0 #_ #IHV0 #K2 #H
  30 @(rdsx_ind … H) -K2 #K0 #HK0 #IHK0 #HK10 #I
  31 @rdsx_intro #Y #HY #HnY
  32 elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
  33 elim (tdeq_dec h o V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
  34 [ /5 width=5 by rdsx_rdeq_trans, lpxs_step_dx, rdeq_pair/
  35 | @(IHV0 … HnV02) -IHV0 -HnV02
  36   [ /2 width=3 by lpxs_cpx_trans/
  37   | /3 width=3 by rdsx_lpx_trans, rdsx_cpx_trans/
  38   | /2 width=3 by lpxs_step_dx/
  39   ]
  40 ]
  41 qed.
  42
  43 (* Basic_2A1: uses: lsx_lref_be *)
  44 lemma rdsx_lref_pair_drops (h) (o) (G):
  45                            ∀K,V. ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄ →
  46                            ∀I,i,L. ⬇*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
  47 #h #o #G #K #V #HV #HK #I #i elim i -i
  48 [ #L #H >(drops_fwd_isid … H) -H /2 width=3 by rdsx_pair_lpxs/
  49 | #i #IH #L #H
  50   elim (drops_inv_bind2_isuni_next … H) -H // #J #Y #HY #H destruct
  51   @(rdsx_lifts … (𝐔❴1❵)) /3 width=6 by drops_refl, drops_drop/ (**) (* full auto fails *)
  52 ]
  53 qed.
  54
  55 (* Main properties **********************************************************)
  56
  57 (* Basic_2A1: uses: csx_lsx *)
  58 theorem csx_rdsx (h) (o): ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
  59 #h #o #G #L #T @(fqup_wf_ind_eq (Ⓕ) … G L T) -G -L -T
  60 #Z #Y #X #IH #G #L * * //
  61 [ #i #HG #HL #HT #H destruct
  62   elim (csx_inv_lref … H) -H [ |*: * ]
  63   [ /2 width=1 by rdsx_lref_atom/
  64   | /2 width=3 by rdsx_lref_unit/
  65   | /4 width=6 by rdsx_lref_pair_drops, fqup_lref/
  66   ]
  67 | #p #I #V #T #HG #HL #HT #H destruct
  68   elim (csx_fwd_bind_unit … H Void) -H /3 width=1 by rdsx_bind_void/
  69 | #I #V #T #HG #HL #HT #H destruct
  70   elim (csx_fwd_flat … H) -H /3 width=1 by rdsx_flat/
  71 ]
  72 qed.