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15 include "basic_2A/notation/relations/lazyeq_7.ma".
16 include "basic_2A/grammar/genv.ma".
17 include "basic_2A/multiple/lleq.ma".
19 (* LAZY EQUIVALENCE FOR CLOSURES ********************************************)
21 inductive fleq (l) (G) (L1) (T): relation3 genv lenv term ≝
22 | fleq_intro: ∀L2. L1 ≡[T, l] L2 → fleq l G L1 T G L2 T
26 "lazy equivalence (closure)"
27 'LazyEq l G1 L1 T1 G2 L2 T2 = (fleq l G1 L1 T1 G2 L2 T2).
29 (* Basic properties *********************************************************)
31 lemma fleq_refl: ∀l. tri_reflexive … (fleq l).
32 /2 width=1 by fleq_intro/ qed.
34 lemma fleq_sym: ∀l. tri_symmetric … (fleq l).
35 #l #G1 #L1 #T1 #G2 #L2 #T2 * /3 width=1 by fleq_intro, lleq_sym/
38 (* Basic inversion lemmas ***************************************************)
40 lemma fleq_inv_gen: ∀G1,G2,L1,L2,T1,T2,l. ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄ →
41 ∧∧ G1 = G2 & L1 ≡[T1, l] L2 & T1 = T2.
42 #G1 #G2 #L1 #L2 #T1 #T2 #l * -G2 -L2 -T2 /2 width=1 by and3_intro/