matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpce.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  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/cpmuwe_cpmuwe.ma".
  16 include "basic_2/rt_conversion/cpce_drops.ma".
  17 include "basic_2/dynamic/cnv_cpmuwe.ma".
  18
  19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  20
  21 (* Properties with context-sensitive parallel eta-conversion for terms ******)
  22
  23 axiom cpce_total_cnv (h) (a) (G) (L):
  24       ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] → ∃T2. ⦃G,L⦄ ⊢ T1 ⬌η[h] T2.
  25 (*
  26 #h #a #G #L #T1 #HT1
  27 lapply (cnv_fwd_csx … HT1) #H
  28 generalize in match HT1; -HT1
  29 @(csx_ind_fpbg … H) -G -L -T1
  30 #G #L * *
  31 [ #s #_ #_ /2 width=2 by cpce_sort, ex_intro/
  32 | #i #H1i #IH #H2i
  33   elim (drops_ldec_dec L i) [ * #K #W #HLK | -H1i -IH #HnX ]
  34   [ lapply (cnv_inv_lref_pair … H2i … HLK) -H2i #H2W
  35     lapply (csx_inv_lref_pair_drops … HLK H1i) -H1i #H1W
  36     elim (cpmuwe_total_csx … H1W) -H1W #X #n #HWX
  37     elim (abst_dec X) [ * | -IH ]
  38     [ #p #V1 #U #H destruct
  39       lapply (cpmuwe_fwd_cpms … HWX) -HWX #HWX
  40       elim (IH G K V1) -IH
  41       [ #V2 #HV12
  42         elim (lifts_total V2 (𝐔❴↑i❵)) #W2 #HVW2
  43         /3 width=12 by cpce_eta_drops, ex_intro/
  44       | /3 width=6 by  cnv_cpms_trans, cnv_fwd_pair_sn/
  45       | /4 width=6 by fqup_cpms_fwd_fpbg, fpbg_fqu_trans, fqup_lref/
  46       ]
  47     | #HnX
  48       @(ex_intro … (#i))
  49       @cpce_zero_drops #n0 #p #K0 #W0 #V0 #U0 #HLK0 #HWU0
  50       lapply (drops_mono … HLK0 … HLK) -i -L #H destruct
  51       lapply (cpmuwe_abst … HWU0) -HWU0 #HWU0
  52       elim (cnv_cpmuwe_mono … H2W … HWU0 … HWX) #_ #H -a -n -n0 -W
  53       elim (tweq_inv_abst_sn … H) -V0 -U0 #V0 #U0 #H destruct
  54       /2 width=4 by/
  55     ]
  56   | /5 width=3 by cpce_zero_drops, ex1_2_intro, ex_intro/
  57   ]
  58 | #l #_ #_ /2 width=2 by cpce_gref, ex_intro/
  59 | #p #I #V1 #T1 #_ #IH #H
  60   elim (cnv_inv_bind … H) -H #HV1 #HT1
  61   elim (IH … HV1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_pair_sn/ ] #V2 #HV12
  62   elim (IH … HT1) [| /4 width=1 by fpb_fpbg, fpb_fqu, fqu_bind_dx/ ] #T2 #HT12
  63   /3 width=2 by cpce_bind, ex_intro/
  64 | #I #V1 #T1 #_ #IH #H
  65   elim (cnv_fwd_flat … H) -H #HV1 #HT1
  66   elim (IH … HV1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_pair_sn/ ] #V2 #HV12
  67   elim (IH … HT1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_flat_dx/ ] #T2 #HT12
  68   /3 width=2 by cpce_flat, ex_intro/
  69 ]
  70 qed-.
  71 *)