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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
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  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_csx.ma".
  16 include "basic_2/rt_equivalence/cpes.ma".
  17 include "basic_2/dynamic/cnv_preserve.ma".
  18
  19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  20
  21 (* Properties with t-unbound whd evaluation on terms ************************)
  22
  23 lemma cnv_cpmuwe_trans (h) (a) (G) (L):
  24       ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
  25       ∀n,T2. ❪G,L❫ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ❪G,L❫ ⊢ T2 ![h,a].
  26 /3 width=4 by cpmuwe_fwd_cpms, cnv_cpms_trans/ qed-.
  27
  28 lemma cnv_R_cpmuwe_total (h) (a) (G) (L):
  29       ∀T1. ❪G,L❫ ⊢ T1 ![h,a] → ∃n. R_cpmuwe h G L T1 n.
  30 /4 width=2 by cnv_fwd_fsb, fsb_inv_csx, R_cpmuwe_total_csx/ qed-.
  31
  32 (* Main inversions with head evaluation for t-bound rt-transition on terms **)
  33
  34 theorem cnv_cpmuwe_mono (h) (a) (G) (L):
  35         ∀T0. ❪G,L❫ ⊢ T0 ![h,a] →
  36         ∀n1,T1. ❪G,L❫ ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
  37         ∀n2,T2. ❪G,L❫ ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
  38         ∧∧ ❪G,L❫ ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ≅ T2.
  39 #h #a #G #L #T0 #HT0 #n1 #T1 * #HT01 #HT1 #n2 #T2 * #HT02 #HT2
  40 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
  41 /4 width=4 by cpms_div, tweq_canc_dx, conj/
  42 qed-.