matita/matita/contribs/lambdadelta/basic_2A/computation/csx_aaa.ma

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  14
  15 include "basic_2A/computation/gcp_aaa.ma".
  16 include "basic_2A/computation/cpxs_aaa.ma".
  17 include "basic_2A/computation/csx_tsts_vector.ma".
  18
  19 (* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
  20
  21 (* Main properties on atomic arity assignment *******************************)
  22
  23 theorem aaa_csx: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
  24 #h #g #G #L #T #A #H
  25 @(gcr_aaa … (csx_gcp h g) (csx_gcr h g) … H)
  26 qed.
  27
  28 (* Advanced eliminators *****************************************************)
  29
  30 fact aaa_ind_csx_aux: ∀h,g,G,L,A. ∀R:predicate term.
  31                       (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
  32                             (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
  33                       ) →
  34                       ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
  35 #h #g #G #L #A #R #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
  36 qed-.
  37
  38 lemma aaa_ind_csx: ∀h,g,G,L,A. ∀R:predicate term.
  39                    (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
  40                          (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
  41                    ) →
  42                    ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
  43 /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
  44
  45 fact aaa_ind_csx_alt_aux: ∀h,g,G,L,A. ∀R:predicate term.
  46                           (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
  47                                 (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
  48                           ) →
  49                           ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
  50 #h #g #G #L #A #R #IH #T #H @(csx_ind_alt … H) -T /4 width=5 by cpxs_aaa_conf/
  51 qed-.
  52
  53 lemma aaa_ind_csx_alt: ∀h,g,G,L,A. ∀R:predicate term.
  54                        (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
  55                              (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
  56                        ) →
  57                        ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
  58 /5 width=9 by aaa_ind_csx_alt_aux, aaa_csx/ qed-.