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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/notation/relations/lazyeq_8.ma".
16 include "basic_2/syntax/genv.ma".
17 include "basic_2/static/lfdeq.ma".
19 (* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
21 inductive ffdeq (h) (o) (G) (L1) (T): relation3 genv lenv term ≝
22 | ffdeq_intro: ∀L2. L1 ≡[h, o, T] L2 → ffdeq h o G L1 T G L2 T
26 "degree-based equivalence on referred entries (closure)"
27 'LazyEq h o G1 L1 T1 G2 L2 T2 = (ffdeq h o G1 L1 T1 G2 L2 T2).
29 (* Basic properties *********************************************************)
31 lemma ffdeq_sym: ∀h,o. tri_symmetric … (ffdeq h o).
32 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1 /3 width=1 by ffdeq_intro, lfdeq_sym/
35 (* Basic inversion lemmas ***************************************************)
37 lemma ffdeq_inv_gen: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≡[h, o] ⦃G2, L2, T2⦄ →
38 ∧∧ G1 = G2 & L1 ≡[h, o, T1] L2 & T1 = T2.
39 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
42 (* Basic_2A1: removed theorems 6:
43 fleq_refl fleq_sym fleq_inv_gen
44 fleq_trans fleq_canc_sn fleq_canc_dx