(* *)
(**************************************************************************)
-include "basic_2/notation/relations/lazyeq_8.ma".
+include "basic_2/notation/relations/stareqsn_8.ma".
include "basic_2/syntax/genv.ma".
include "basic_2/static/lfdeq.ma".
(* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
-inductive ffdeq (h) (o) (G) (L1) (T): relation3 genv lenv term ≝
-| ffdeq_intro: ∀L2. L1 ≡[h, o, T] L2 → ffdeq h o G L1 T G L2 T
+inductive ffdeq (h) (o) (G) (L1) (T1): relation3 genv lenv term ≝
+| ffdeq_intro_sn: ∀L2,T2. L1 ≛[h, o, T1] L2 → T1 ≛[h, o] T2 →
+ ffdeq h o G L1 T1 G L2 T2
.
interpretation
"degree-based equivalence on referred entries (closure)"
- 'LazyEq h o G1 L1 T1 G2 L2 T2 = (ffdeq h o G1 L1 T1 G2 L2 T2).
+ 'StarEqSn h o G1 L1 T1 G2 L2 T2 = (ffdeq h o G1 L1 T1 G2 L2 T2).
-(* Basic properties *********************************************************)
+(* Basic_properties *********************************************************)
-lemma ffdeq_sym: ∀h,o. tri_symmetric … (ffdeq h o).
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1 /3 width=1 by ffdeq_intro, lfdeq_sym/
-qed-.
+lemma ffdeq_intro_dx (h) (o) (G): ∀L1,L2,T2. L1 ≛[h, o, T2] L2 →
+ ∀T1. T1 ≛[h, o] T2 → ⦃G, L1, T1⦄ ≛[h, o] ⦃G, L2, T2⦄.
+/3 width=3 by ffdeq_intro_sn, tdeq_lfdeq_div/ qed.
(* Basic inversion lemmas ***************************************************)
-lemma ffdeq_inv_gen: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≡[h, o] ⦃G2, L2, T2⦄ →
- ∧∧ G1 = G2 & L1 ≡[h, o, T1] L2 & T1 = T2.
+lemma ffdeq_inv_gen_sn: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
+ ∧∧ G1 = G2 & L1 ≛[h, o, T1] L2 & T1 ≛[h, o] T2.
#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
qed-.
+lemma ffdeq_inv_gen_dx: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
+ ∧∧ G1 = G2 & L1 ≛[h, o, T2] L2 & T1 ≛[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+/3 width=3 by tdeq_lfdeq_conf, and3_intro/
+qed-.
+
(* Basic_2A1: removed theorems 6:
fleq_refl fleq_sym fleq_inv_gen
fleq_trans fleq_canc_sn fleq_canc_dx