matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_tdeq.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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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 "static_2/syntax/tdeq.ma".
  16 include "basic_2/rt_transition/cpm_drops.ma".
  17
  18 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
  19
  20 (* Inversion lemmas with sort-irrelevant equivalence for terms **************)
  21
  22 lemma cpm_tdeq_inv_lref_sn (n) (h) (G) (L) (i):
  23                            ∀X.  ⦃G,L⦄ ⊢ #i ➡[n,h] X → #i ≛ X →
  24                            ∧∧ X = #i & n = 0.
  25 #n #h #G #L #i #X #H1 #H2
  26 lapply (tdeq_inv_lref1 … H2) -H2 #H destruct
  27 elim (cpm_inv_lref1_drops … H1) -H1 // * [| #m ]
  28 #K #V1 #V2 #_ #_ #H -V1
  29 elim (lifts_inv_lref2_uni_lt … H) -H //
  30 qed-.
  31
  32 lemma cpm_tdeq_inv_atom_sn (n) (h) (I) (G) (L):
  33                            ∀X. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] X → ⓪{I} ≛ X →
  34                            ∨∨ ∧∧ X = ⓪{I} & n = 0
  35                             | ∃∃s. X = ⋆(next h s) & I = Sort s & n = 1.
  36 #n #h * #s #G #L #X #H1 #H2
  37 [ elim (cpm_inv_sort1 … H1) -H1
  38   cases n -n [| #n ] #H #Hn destruct -H2
  39   [ /3 width=1 by or_introl, conj/
  40   | <(le_n_O_to_eq n) [| /2 width=3 by le_S_S_to_le/ ] -n
  41     /3 width=3 by ex3_intro, or_intror/
  42   ]
  43 | elim (cpm_tdeq_inv_lref_sn … H1 H2) -H1 -H2 /3 width=1 by or_introl, conj/
  44 | elim (cpm_inv_gref1 … H1) -H1 -H2 /3 width=1 by or_introl, conj/
  45 ]
  46 qed-.