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

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/rt_equivalence/cpcs_cprs.ma".
  16 include "basic_2/dynamic/cnv_preserve.ma".
  17
  18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  19
  20 (* Forward lemmas with r-equivalence ****************************************)
  21
  22 lemma cnv_cpms_conf_eq (a) (h) (n) (G) (L):
  23       ∀T. ⦃G,L⦄ ⊢ T ![a,h] →
  24       ∀T1. ⦃G,L⦄ ⊢ T ➡*[n,h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ➡*[n,h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2.
  25 #a #h #n #G #L #T #HT #T1 #HT1 #T2 #HT2
  26 elim (cnv_cpms_conf … HT … HT1 … HT2) -T <minus_n_n #T #HT1 #HT2
  27 /2 width=3 by cprs_div/
  28 qed-.
  29
  30 lemma cnv_cpms_fwd_appl_sn_decompose (a) (h) (G) (L):
  31       ∀V,T. ⦃G,L⦄ ⊢ ⓐV.T ![a,h] → ∀n,X. ⦃G,L⦄ ⊢ ⓐV.T ➡*[n,h] X →
  32       ∃∃U. ⦃G,L⦄ ⊢ T ![a,h] & ⦃G,L⦄ ⊢ T ➡*[n,h] U & ⦃G,L⦄ ⊢ ⓐV.U ⬌*[h] X.
  33 #a #h #G #L #V #T #H0 #n #X #HX
  34 elim (cnv_inv_appl … H0) #m #p #W #U #_ #_ #HT #_ #_ -m -p -W -U
  35 elim (cnv_fwd_cpms_total … h n … HT) #U #HTU
  36 lapply (cpms_appl_dx … V V … HTU) [ // ] #H
  37 /3 width=8 by cnv_cpms_conf_eq, ex3_intro/
  38 qed-.