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

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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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/nta.ma".
  17
  18 (* NATIVE TYPE ASSIGNMENT FOR TERMS *****************************************)
  19
  20 (* Properties with r-equivalence for terms **********************************)
  21
  22 lemma nta_conv_cnv (a) (h) (G) (L) (T):
  23                    ∀U1. ⦃G,L⦄ ⊢ T :[a,h] U1 →
  24                    ∀U2. ⦃G,L⦄  ⊢ U1 ⬌*[h] U2 → ⦃G,L⦄ ⊢ U2 ![a,h] → ⦃G,L⦄ ⊢ T :[a,h] U2.
  25 #a #h #G #L #T #U1 #H1 #U2 #HU12 #HU2
  26 elim (cnv_inv_cast … H1) -H1 #X1 #HU1 #HT #HUX1 #HTX1
  27 lapply (cpcs_cprs_conf … HUX1 … HU12) -U1 #H
  28 elim (cpcs_inv_cprs … H) -H #X2 #HX12 #HU12
  29 /3 width=5 by cnv_cast, cpms_cprs_trans/
  30 qed-.
  31
  32 (* Basic_1: was by definition: ty3_conv *)
  33 (* Basic_2A1: was by definition: nta_conv ntaa_conv *)
  34 lemma nta_conv (a) (h) (G) (L) (T):
  35                ∀U1. ⦃G,L⦄ ⊢ T :[a,h] U1 →
  36                ∀U2. ⦃G,L⦄  ⊢ U1 ⬌*[h] U2 →
  37                ∀W2. ⦃G,L⦄ ⊢ U2 :[a,h] W2 → ⦃G,L⦄ ⊢ T :[a,h] U2.
  38 #a #h #G #L #T #U1 #H1 #U2 #HU12 #W2 #H2
  39 /3 width=3 by nta_conv_cnv, nta_fwd_cnv_sn/
  40 qed-.
  41
  42 (* Inversion lemmas with r-equivalence for terms ***************************)
  43
  44 (* Basic_1: was: ty3_gen_sort *)
  45 (* Basic_2A1: was: nta_inv_sort1 *)
  46 lemma nta_inv_sort_sn (a) (h) (G) (L) (X2):
  47       ∀s. ⦃G,L⦄ ⊢ ⋆s :[a,h] X2 → ⦃G,L⦄ ⊢ ⋆(next h s) ⬌*[h] X2.
  48 #a #h #G #L #X2 #s #H
  49 elim (cnv_inv_cast … H) -H #X1 #HX2 #_ #HX21 #H
  50 lapply (cpms_inv_sort1 … H) -H #H destruct
  51 /2 width=1 by cpcs_cprs_sn/
  52 qed-.
  53