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basic_2: stronger supclosure allows better inversion lemmas
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14
15 include "basic_2/notation/relations/lazyeq_6.ma".
16 include "basic_2/static/lfeq_lreq.ma".
17 include "basic_2/static/lfeq_fqup.ma".
18
19 (* EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *****************************)
20
21 inductive ffeq (G) (L1) (T): relation3 genv lenv term ≝
22 | fleq_intro: ∀L2. L1 ≡[T] L2 → ffeq G L1 T G L2 T
23 .
24
25 interpretation
26    "equivalence on referred entries (closure)"
27    'LazyEq G1 L1 T1 G2 L2 T2 = (ffeq G1 L1 T1 G2 L2 T2).
28
29 (* Basic properties *********************************************************)
30
31 lemma ffeq_refl: tri_reflexive … ffeq.
32 /2 width=1 by fleq_intro/ qed.
33
34 lemma ffeq_sym: tri_symmetric … ffeq.
35 #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1 /3 width=1 by fleq_intro, lfeq_sym/
36 qed-.
37
38 (* Basic inversion lemmas ***************************************************)
39
40 lemma ffeq_inv_gen: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≡ ⦃G2, L2, T2⦄ →
41                     ∧∧ G1 = G2 & L1 ≡[T1] L2 & T1 = T2.
42 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
43 qed-.
44
45 (* Basic_2A1: removed theorems 6:
46               fleq_refl fleq_sym fleq_inv_gen
47               fleq_trans fleq_canc_sn fleq_canc_dx
48 *)