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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_2A/multiple/llpx_sn_lreq.ma".
16 include "basic_2A/multiple/lleq.ma".
18 (* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
20 (* Properties on equivalence for local environments *************************)
22 lemma lreq_lleq_trans: ∀L2,L,T,l. L2 ≡[T, l] L →
23 ∀L1. L1 ⩬[l, ∞] L2 → L1 ≡[T, l] L.
24 /2 width=3 by lreq_llpx_sn_trans/ qed-.
26 lemma lleq_lreq_trans: ∀L,L1,T,l. L ≡[T, l] L1 →
27 ∀L2. L1 ⩬[l, ∞] L2 → L ≡[T, l] L2.
28 /2 width=3 by llpx_sn_lreq_trans/ qed-.
30 lemma lleq_lreq_repl: ∀L1,L2,T,l. L1 ≡[T, l] L2 → ∀K1. K1 ⩬[l, ∞] L1 →
31 ∀K2. L2 ⩬[l, ∞] K2 → K1 ≡[T, l] K2.
32 /2 width=5 by llpx_sn_lreq_repl/ qed-.
34 lemma lleq_bind_repl_SO: ∀I1,I2,L1,L2,V1,V2,T. L1.ⓑ{I1}V1 ≡[T, 0] L2.ⓑ{I2}V2 →
35 ∀J1,J2,W1,W2. L1.ⓑ{J1}W1 ≡[T, 1] L2.ⓑ{J2}W2.
36 /2 width=5 by llpx_sn_bind_repl_SO/ qed-.