matita/matita/contribs/lambdadelta/basic_2/etc/sdsx/sdsx_rdsx.etc

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  14
  15 include "static_2/relocation/scl.ma".
  16 include "basic_2/rt_computation/rdsx_drops.ma".
  17 include "basic_2/rt_computation/rdsx_lpxs.ma".
  18 include "basic_2/rt_computation/sdsx.ma".
  19
  20 axiom pippo (h) (f) (G) (V:term):
  21       ∀L1. G ⊢ ⬈*[h,V] 𝐒⦃L1⦄ →
  22       ∀L2. L1 ⊐ⓧ[f] L2 → G ⊢ ⬈*[h,V] 𝐒⦃L2⦄.
  23
  24
  25 (* STRONGLY NORMALIZING SELECTED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
  26
  27 (* Properties with strongly normalizing referred local environments *********)
  28
  29 (* Basic_2A1: uses: lsx_cpx_trans_lcosx *)
  30 lemma rdsx_cpx_trans_sdsx (h):
  31       ∀G,L0,T1,T2. ⦃G,L0⦄ ⊢ T1 ⬈[h] T2 →
  32       ∀f. G ⊢ ⬈*[h,f] 𝐒⦃L0⦄ → ∀L. L0 ⊐ⓧ[f] L →
  33       G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
  34 #h #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2
  35 [ //
  36 | //
  37 | #I #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #g #H1 #Y #H2 #H3
  38   elim (sdsx_inv_pair_gen … H1) -H1 *
  39   [ #f #HK0 #H destruct
  40     elim (scl_inv_push_sn … H2) -H2 #K #HK #H destruct
  41     /4 width=8 by rdsx_lifts, rdsx_fwd_pair, drops_refl, drops_drop/
  42   | #f #HV1 #HK0 #H destruct
  43     elim (scl_inv_next_sn … H2) -H2 #K #HK #H destruct
  44     /4 width=8 by pippo, rdsx_lifts, drops_refl, drops_drop/
  45   ]
  46 | #I0 #G #K0 #T #U #i #_ #IH #HTU #g #H1 #Y #H2 #H3
  47   lapply (sdsx_fwd_bind … H1) -H1 #HK0
  48   elim (scl_fwd_bind_sn … H2) -H2 #I #K #HK #H destruct
  49   /6 width=8 by rdsx_inv_lifts, rdsx_lifts, drops_refl, drops_drop/
  50 | #p #I #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #H1 #L #H2 #H3
  51   elim (rdsx_inv_bind_void … H3) -H3 #HV1 #HT1
  52   @rdsx_bind_void
  53   [ /2 width=3 by/
  54   | @(IHT12 (↑f) … HT1)
  55     [ @(sdsx_pair … H1)
  56     | /2 width=1 by scl_next/
  57
  58   /4 width=2 by lsubsx_pair, rdsx_bind_void/
  59 | #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
  60   elim (rdsx_inv_flat … HL) -HL /3 width=2 by rdsx_flat/
  61 | #G #L0 #V #U1 #T1 #T2 #HTU1 #_ #IHT12 #f #L #HL0 #HL
  62   elim (rdsx_inv_bind … HL) -HL #HV #HU1
  63   /5 width=8 by rdsx_inv_lifts, drops_refl, drops_drop/
  64 | #G #L0 #V #T1 #T2 #_ #IHT12 #f #L #HL0 #HL
  65   elim (rdsx_inv_flat … HL) -HL /2 width=2 by/
  66 | #G #L0 #V1 #V2 #T #_ #IHV12 #f #L #HL0 #HL
  67   elim (rdsx_inv_flat … HL) -HL /2 width=2 by/
  68 | #p #G #L0 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #f #L #HL0 #HL
  69   elim (rdsx_inv_flat … HL) -HL #HV1 #HL
  70   elim (rdsx_inv_bind … HL) -HL #HW1 #HT1
  71   /4 width=2 by lsubsx_pair, rdsx_bind_void, rdsx_flat/
  72 | #p #G #L0 #V1 #V2 #U2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #HVU2 #f #L #HL0 #HL
  73   elim (rdsx_inv_flat … HL) -HL #HV1 #HL
  74   elim (rdsx_inv_bind … HL) -HL #HW1 #HT1
  75   /6 width=8 by lsubsx_pair, rdsx_lifts, rdsx_bind_void, rdsx_flat, drops_refl, drops_drop/
  76 ]
  77 qed-.
  78
  79 (* Advanced properties of strongly normalizing referred local environments **)
  80
  81 (* Basic_2A1: uses: lsx_cpx_trans_O *)
  82 lemma rdsx_cpx_trans (h):
  83       ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 →
  84       G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
  85 /3 width=6 by rdsx_cpx_trans_lsubsx, lsubsx_refl/ qed-.
  86
  87 lemma rdsx_cpxs_trans (h):
  88       ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 →
  89       G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
  90 #h #G #L #T1 #T2 #H
  91 @(cpxs_ind_dx ???????? H) -T1 //
  92 /3 width=3 by rdsx_cpx_trans/
  93 qed-.
  94 *)