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14
15 include "static_2/notation/relations/stareqsn_6.ma".
16 include "static_2/syntax/genv.ma".
17 include "static_2/static/rdeq.ma".
18
19 (* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
20
21 inductive fdeq (G) (L1) (T1): relation3 genv lenv term ≝
22 | fdeq_intro_sn: ∀L2,T2. L1 ≛[T1] L2 → T1 ≛ T2 →
23                  fdeq G L1 T1 G L2 T2
24 .
25
26 interpretation
27    "sort-irrelevant equivalence on referred entries (closure)"
28    'StarEqSn G1 L1 T1 G2 L2 T2 = (fdeq G1 L1 T1 G2 L2 T2).
29
30 (* Basic_properties *********************************************************)
31
32 lemma fdeq_intro_dx (G): ∀L1,L2,T2. L1 ≛[T2] L2 →
33                          ∀T1. T1 ≛ T2 → ⦃G, L1, T1⦄ ≛ ⦃G, L2, T2⦄.
34 /3 width=3 by fdeq_intro_sn, tdeq_rdeq_div/ qed.
35
36 (* Basic inversion lemmas ***************************************************)
37
38 lemma fdeq_inv_gen_sn: ∀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 fdeq_inv_gen_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T2⦄ →
44                        ∧∧ G1 = G2 & L1 ≛[T2] L2 & T1 ≛ T2.
45 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
46 /3 width=3 by tdeq_rdeq_conf, and3_intro/
47 qed-.
48
49 (* Basic_2A1: removed theorems 6:
50               fleq_refl fleq_sym fleq_inv_gen
51               fleq_trans fleq_canc_sn fleq_canc_dx
52 *)