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

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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_transition/cpx_lsubr.ma".
  16 include "basic_2/rt_computation/csx_csx.ma".
  17
  18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 fact csx_appl_beta_aux: ∀h,p,G,L,U1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃U1⦄ →
  23                         ∀V,W,T1. U1 = ⓓ{p}ⓝW.V.T1 → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.ⓛ{p}W.T1⦄.
  24 #h #p #G #L #X #H @(csx_ind … H) -X
  25 #X #HT1 #IHT1 #V #W #T1 #H1 destruct
  26 @csx_intro #X #H1 #H2
  27 elim (cpx_inv_appl1 … H1) -H1 *
  28 [ -HT1 #V0 #Y #HLV0 #H #H0 destruct
  29   elim (cpx_inv_abst1 … H) -H #W0 #T0 #HLW0 #HLT0 #H destruct
  30   @IHT1 -IHT1 [4: // | skip ]
  31   [ lapply (lsubr_cpx_trans … HLT0 (L.ⓓⓝW.V) ?) -HLT0 -H2
  32     /3 width=1 by cpx_bind, cpx_flat, lsubr_beta/
  33   | #H elim (tdeq_inv_pair … H) -H
  34     #_ #H elim (tdeq_inv_pair … H) -H
  35     #_ /4 width=1 by tdeq_pair/
  36   ]
  37 | -IHT1 -H2 #q #V0 #W0 #W2 #T0 #T2 #HLV0 #HLW02 #HLT02 #H1 #H3 destruct
  38   lapply (lsubr_cpx_trans … HLT02 (L.ⓓⓝW0.V) ?) -HLT02
  39   /4 width=5 by csx_cpx_trans, cpx_bind, cpx_flat, lsubr_beta/
  40 | -HT1 -IHT1 -H2 #q #V0 #V1 #W0 #W1 #T0 #T3 #_ #_ #_ #_ #H destruct
  41 ]
  42 qed-.
  43
  44 (* Basic_1: was just: sn3_beta *)
  45 lemma csx_appl_beta: ∀h,p,G,L,V,W,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}ⓝW.V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.ⓛ{p}W.T⦄.
  46 /2 width=3 by csx_appl_beta_aux/ qed.
  47
  48 (* Advanced forward lemmas **************************************************)
  49
  50 fact csx_fwd_bind_dx_unit_aux: ∀h,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
  51                                ∀p,I,J,V,T. U = ⓑ{p,I}V.T → ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
  52 #h #G #L #U #H elim H -H #U0 #_ #IH #p #I #J #V #T #H destruct
  53 @csx_intro #T2 #HLT2 #HT2
  54 @(IH (ⓑ{p,I}V.T2)) -IH /2 width=4 by cpx_bind_unit/ -HLT2
  55 #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
  56 qed-.
  57
  58 lemma csx_fwd_bind_dx_unit: ∀h,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
  59                             ∀J. ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
  60 /2 width=6 by csx_fwd_bind_dx_unit_aux/ qed-.
  61
  62 lemma csx_fwd_bind_unit: ∀h,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
  63                          ∀J. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ ∧ ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
  64 /3 width=4 by csx_fwd_pair_sn, csx_fwd_bind_dx_unit, conj/ qed-.