matita/matita/contribs/lambdadelta/basic_2/etc/cpce/lsubv_cpce_1.etc

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/rt_conversion/cpce.ma".
  16 include "basic_2/rt_equivalence/cpcs.ma".
  17 include "basic_2/dynamic/lsubv.ma".
  18
  19 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
  20
  21 lemma lsubv_inv_unit_dx (h) (a) (G):
  22       ∀I,L1,K2. G ⊢ L1 ⫃![h,a] K2.ⓤ{I} →
  23       ∃∃K1. G ⊢ K1 ⫃![h,a] K2 & L1 = K1.ⓤ{I}.
  24 #h #a #G #I #L1 #K2 #H
  25 elim (lsubv_inv_bind_dx … H) -H // *
  26 #K1 #XW #XV #_ #_ #H1 #H2 destruct
  27 qed-.
  28
  29 lemma lsubv_inv_abbr_dx (h) (a) (G):
  30       ∀L1,K2,V. G ⊢ L1 ⫃![h,a] K2.ⓓV →
  31       ∃∃K1. G ⊢ K1 ⫃![h,a] K2 & L1 = K1.ⓓV.
  32 #h #a #G #L1 #K2 #V #H
  33 elim (lsubv_inv_bind_dx … H) -H // *
  34 #K1 #XW #XV #_ #_ #H1 #H2 destruct
  35 qed-.
  36
  37 lemma lsubv_cpce_trans_cpcs (h) (a) (G) (T0):
  38       ∀L2,T2. ⦃G,L2⦄ ⊢ T0 ⬌η[h] T2 → ∀L1. G ⊢ L1 ⫃![h,a] L2 →
  39       ∃∃T1. ⦃G,L1⦄ ⊢ T0 ⬌η[h] T1 & ⦃G,L1⦄ ⊢ T1 ⬌*[h] T2.
  40 #h #a #G #T0 #L2 #T2 #H elim H -G -L2 -T0 -T2
  41 [ #G #L2 #s #L1 #HL12
  42   /2 width=3 by cpce_sort, ex2_intro/
  43 | #G #i #Y1 #HY1
  44   lapply (lsubv_inv_atom2 … HY1) -HY1 #H destruct
  45    /2 width=3 by cpce_atom, ex2_intro/
  46 | #I #G #K2 #Y1 #HY1
  47   elim (lsubv_inv_unit_dx … HY1) -HY1 #K2 #_ #H destruct
  48   /2 width=3 by cpce_unit, ex2_intro/
  49 | #G #K2 #V2 #Y1 #HY1
  50   elim (lsubv_inv_abbr_dx … HY1) -HY1 #K2 #_ #H destruct
  51   /2 width=3 by cpce_ldef, ex2_intro/
  52 | #G #K2 #W2 #HW2 #Y1 #HY1
  53   elim (lsubv_inv_bind_dx … HY1) -HY1 *
  54   [ #K1 #HK12 #H destruct
  55     @(ex2_intro … (#0)) [| // ]
  56     @cpce_ldec #n #p #V2 #U2 #HWU2