matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma

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  14
  15 include "basic_2/notation/relations/lazyeqsn_3.ma".
  16 include "basic_2/static/lfxs.ma".
  17
  18 (* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
  19
  20 (* Basic_2A1: was: lleq *)
  21 definition lfeq: relation3 term lenv lenv ≝
  22                  lfxs ceq.
  23
  24 interpretation
  25    "syntactic equivalence on referred entries (local environment)"
  26    'LazyEqSn T L1 L2 = (lfeq T L1 L2).
  27
  28 (* Basic_2A1: uses: lleq_transitive *)
  29 definition lfeq_transitive: predicate (relation3 lenv term term) ≝
  30            λR. ∀L2,T1,T2. R L2 T1 T2 → ∀L1. L1 ≡[T1] L2 → R L1 T1 T2.
  31
  32 (* Basic_properties *********************************************************)
  33
  34 lemma lfxs_transitive_lfeq: ∀R. lfxs_transitive ceq R R → lfeq_transitive R.
  35 /2 width=5 by/ qed.
  36
  37 (* Basic inversion lemmas ***************************************************)
  38
  39 lemma lfeq_transitive_inv_lfxs: ∀R. lfeq_transitive R → lfxs_transitive ceq R R.
  40 /2 width=3 by/ qed-.
  41
  42 (* Basic forward lemmas *****************************************************)
  43
  44 (* Basic_2A1: was: llpx_sn_lrefl *)
  45 (* Note: this should have been lleq_fwd_llpx_sn *)
  46 lemma lfeq_fwd_lfxs: ∀R. c_reflexive … R →
  47                      ∀L1,L2,T. L1 ≡[T] L2 → L1 ⪤*[R, T] L2.
  48 #R #HR #L1 #L2 #T * #f #Hf #HL12
  49 /4 width=7 by lexs_co, cext2_co, ex2_intro/
  50 qed-.
  51
  52 (* Basic_2A1: removed theorems 10:
  53               lleq_ind lleq_fwd_lref
  54               lleq_fwd_drop_sn lleq_fwd_drop_dx
  55               lleq_skip lleq_lref lleq_free
  56               lleq_Y lleq_ge_up lleq_ge
  57
  58 *)