matita/matita/contribs/lambdadelta/static_2/static/feqx.ma

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  14
  15 include "static_2/notation/relations/approxeqsn_6.ma".
  16 include "static_2/syntax/teqx.ma".
  17 include "static_2/static/feqg.ma".
  18
  19 (* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
  20
  21 definition feqx: relation6 genv lenv term genv lenv term ≝
  22            feqg sfull.
  23
  24 interpretation
  25   "sort-irrelevant equivalence on referred entries (closure)"
  26   'ApproxEqSn G1 L1 T1 G2 L2 T2 = (feqx G1 L1 T1 G2 L2 T2).
  27
  28 (* Basic_properties *********************************************************)
  29 (*
  30 lemma feqx_intro_dx (G):
  31       ∀L1,L2,T2. L1 ≛[T2] L2 →
  32       ∀T1. T1 ≛ T2 → ❪G,L1,T1❫ ≛ ❪G,L2,T2❫.
  33 /3 width=3 by feqx_intro_sn, teqx_reqx_div/ qed.
  34
  35 (* Basic inversion lemmas ***************************************************)
  36
  37 lemma feqx_inv_gen_sn:
  38       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ →
  39       ∧∧ G1 = G2 & L1 ≛[T1] L2 & T1 ≛ T2.
  40 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
  41 qed-.
  42
  43 lemma feqx_inv_gen_dx:
  44       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ →
  45       ∧∧ G1 = G2 & L1 ≛[T2] L2 & T1 ≛ T2.
  46 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  47 /3 width=3 by teqx_reqx_conf_sn, and3_intro/
  48 qed-.
  49 *)
  50 (* Basic_2A1: removed theorems 6:
  51               fleq_refl fleq_sym fleq_inv_gen
  52               fleq_trans fleq_canc_sn fleq_canc_dx
  53 *)