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

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_computation/cpms_cnh.ma".
  16 include "basic_2/rt_computation/cpmhe_csx.ma".
  17 include "basic_2/rt_equivalence/cpes.ma".
  18 include "basic_2/dynamic/cnv_preserve.ma".
  19
  20 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  21
  22 (* Properties with head evaluation for t-bound rt-transition on terms *******)
  23
  24 lemma cnv_cpmhe_trans (a) (h) (G) (L):
  25       ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
  26       ∀T2,n. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄ → ⦃G,L⦄ ⊢ T2 ![a,h].
  27 /3 width=4 by cpmhe_fwd_cpms, cnv_cpms_trans/ qed-.
  28
  29 lemma cnv_R_cpmhe_total (a) (h) (G) (L):
  30       ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∃n. R_cpmhe h G L T1 n.
  31 /4 width=2 by cnv_fwd_fsb, fsb_inv_csx, R_cpmhe_total_csx/ qed-.
  32
  33 axiom cnv_R_cpmhe_dec (a) (h) (G) (L):
  34       ∀T. ⦃G,L⦄ ⊢ T ![a,h] → ∀n. Decidable (R_cpmhe h G L T n).
  35
  36 (* Main inversions with head evaluation for t-bound rt-transition on terms **)
  37
  38 theorem cnv_cpmhe_mono (a) (h) (G) (L):
  39         ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*[h,n1] 𝐍*⦃T1⦄ →
  40         ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*[h,n2] 𝐍*⦃T2⦄ →
  41         ∧∧ ⦃G,L⦄ ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ⩳ T2.
  42 #a #h #G #L #T0 #HT0 #T1 #n1 * #HT01 #HT1 #T2 #n2 * #HT02 #HT2
  43 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
  44 /4 width=8 by cpms_div, cpms_inv_cnh_sn, theq_canc_dx, conj/
  45 qed-.