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15 include "basic_2/computation/lpxs_lleq.ma".
16 include "basic_2/computation/lsx.ma".
18 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
20 (* Advanced properties ******************************************************)
22 lemma lsx_lleq_trans: ∀h,g,T,G,L1. G ⊢ ⋕⬊*[h, g, T] L1 →
23 ∀L2. L1 ⋕[0, T] L2 → G ⊢ ⋕⬊*[h, g, T] L2.
24 #h #g #T #G #L1 #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
25 @lsx_intro #L #HL2 #HnT elim (lleq_lpxs_trans_nlleq … HL12 … HL2 HnT) -L2 /3 width=4 by/
28 lemma lsx_lpxs_trans: ∀h,g,T,G,L1. G ⊢ ⋕⬊*[h, g, T] L1 →
29 ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → G ⊢ ⋕⬊*[h, g, T] L2.
30 #h #g #T #G #L1 #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
31 elim (lleq_dec T L1 L2 0) /3 width=4 by lsx_lleq_trans/