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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "static_2/notation/relations/stareqsn_8.ma".
16 include "static_2/syntax/genv.ma".
17 include "static_2/static/rdeq.ma".
19 (* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
21 inductive fdeq (h) (o) (G) (L1) (T1): relation3 genv lenv term ≝
22 | fdeq_intro_sn: ∀L2,T2. L1 ≛[h, o, T1] L2 → T1 ≛[h, o] T2 →
23 fdeq h o G L1 T1 G L2 T2
27 "degree-based equivalence on referred entries (closure)"
28 'StarEqSn h o G1 L1 T1 G2 L2 T2 = (fdeq h o G1 L1 T1 G2 L2 T2).
30 (* Basic_properties *********************************************************)
32 lemma fdeq_intro_dx (h) (o) (G): ∀L1,L2,T2. L1 ≛[h, o, T2] L2 →
33 ∀T1. T1 ≛[h, o] T2 → ⦃G, L1, T1⦄ ≛[h, o] ⦃G, L2, T2⦄.
34 /3 width=3 by fdeq_intro_sn, tdeq_rdeq_div/ qed.
36 (* Basic inversion lemmas ***************************************************)
38 lemma fdeq_inv_gen_sn: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
39 ∧∧ G1 = G2 & L1 ≛[h, o, T1] L2 & T1 ≛[h, o] T2.
40 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
43 lemma fdeq_inv_gen_dx: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
44 ∧∧ G1 = G2 & L1 ≛[h, o, T2] L2 & T1 ≛[h, o] T2.
45 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
46 /3 width=3 by tdeq_rdeq_conf, and3_intro/
49 (* Basic_2A1: removed theorems 6:
50 fleq_refl fleq_sym fleq_inv_gen
51 fleq_trans fleq_canc_sn fleq_canc_dx