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14
15 include "basic_2/substitution/lleq_ldrop.ma".
16 include "basic_2/computation/llsx.ma".
17
18 (* LAZY SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS *****************)
19
20 (* Advanced properties ******************************************************)
21
22 lemma llsx_lref_free: ∀h,g,G,L,d,i. |L| ≤ i → G ⊢ ⋕⬊*[h, g, #i, d] L.
23 #h #g #G #L1 #d #i #HL1 @llsx_intro
24 #L2 #HL12 #H elim H -H
25 /4 width=8 by llpx_fwd_length, lleq_free, le_repl_sn_conf_aux/
26 qed.
27
28 lemma llsx_lref_skip: ∀h,g,G,L,d,i. yinj i < d → G ⊢ ⋕⬊*[h, g, #i, d] L.
29 #h #g #G #L1 #d #i #HL1 @llsx_intro
30 #L2 #HL12 #H elim H -H
31 /3 width=6 by llpx_fwd_length, lleq_skip/
32 qed.