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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/reduction/cpx_lleq.ma".
16 include "basic_2/computation/csx.ma".
18 (* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
20 (* Properties on lazy equivalence for local environments ********************)
22 lemma csx_lleq_conf: ∀h,g,G,L1,T. ⦃G, L1⦄ ⊢ ⬊*[h, g] T →
23 ∀L2. L1 ⋕[T, 0] L2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T.
24 #h #g #G #L1 #T #H @(csx_ind … H) -T
25 /4 width=6 by csx_intro, cpx_lleq_conf_dx, lleq_cpx_trans/
28 lemma csx_lleq_trans: ∀h,g,G,L1,L2,T.
29 L1 ⋕[T, 0] L2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T → ⦃G, L1⦄ ⊢ ⬊*[h, g] T.
30 /3 width=3 by csx_lleq_conf, lleq_sym/ qed-.