matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma

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  14
  15 include "basic_2/static/lfxs_fqup.ma".
  16 include "basic_2/i_static/tc_lfxs.ma".
  17
  18 (* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma tc_lfxs_refl: ∀R. (∀L. reflexive … (R L)) → ∀T. reflexive … (tc_lfxs R T).
  23 /3 width=1 by lfxs_refl, inj/ qed.
  24
  25 (* Basic_2A1: uses: TC_lpx_sn_pair TC_lpx_sn_pair_refl *)
  26 lemma tc_lfxs_pair: ∀R. (∀L. reflexive … (R L)) →
  27                     ∀L,V1,V2. LTC … R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⪤**[R, T] L.ⓑ{I}V2.
  28 #R #HR #L #V1 #V2 #H elim H -V2
  29 /3 width=3 by tc_lfxs_step_dx, lfxs_pair, inj/
  30 qed.
  31
  32 (* Advanced eliminators *****************************************************)
  33
  34 lemma tc_lfxs_ind_sn: ∀R. (∀L. reflexive … (R L)) →
  35                       ∀L1,T. ∀R0:predicate …. R0 L1 →
  36                       (∀L,L2. L1 ⪤**[R, T] L → L ⪤*[R, T] L2 → R0 L → R0 L2) →
  37                       ∀L2. L1 ⪤**[R, T] L2 → R0 L2.
  38 #R #HR #L1 #T #R0 #HL1 #IHL1 #L2 #HL12
  39 @(TC_star_ind … HL1 IHL1 … HL12) /2 width=1 by lfxs_refl/
  40 qed-.
  41
  42 lemma tc_lfxs_ind_dx: ∀R. (∀L. reflexive … (R L)) →
  43                       ∀L2,T. ∀R0:predicate …. R0 L2 →
  44                       (∀L1,L. L1 ⪤*[R, T] L → L ⪤**[R, T] L2 → R0 L → R0 L1) →
  45                       ∀L1. L1 ⪤**[R, T] L2 → R0 L1.
  46 #R #HR #L2 #R0 #HL2 #IHL2 #L1 #HL12
  47 @(TC_star_ind_dx … HL2 IHL2 … HL12) /2 width=4 by lfxs_refl/
  48 qed-.