+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/multiple/llpx_sn_lreq.ma".
-include "basic_2/multiple/lleq.ma".
-
-(* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
-
-(* Properties on equivalence for local environments *************************)
-
-lemma lreq_lleq_trans: ∀L2,L,T,l. L2 ≡[T, l] L →
- ∀L1. L1 ⩬[l, ∞] L2 → L1 ≡[T, l] L.
-/2 width=3 by lreq_llpx_sn_trans/ qed-.
-
-lemma lleq_lreq_trans: ∀L,L1,T,l. L ≡[T, l] L1 →
- ∀L2. L1 ⩬[l, ∞] L2 → L ≡[T, l] L2.
-/2 width=3 by llpx_sn_lreq_trans/ qed-.
-
-lemma lleq_lreq_repl: ∀L1,L2,T,l. L1 ≡[T, l] L2 → ∀K1. K1 ⩬[l, ∞] L1 →
- ∀K2. L2 ⩬[l, ∞] K2 → K1 ≡[T, l] K2.
-/2 width=5 by llpx_sn_lreq_repl/ qed-.
-
-lemma lleq_bind_repl_SO: ∀I1,I2,L1,L2,V1,V2,T. L1.ⓑ{I1}V1 ≡[T, 0] L2.ⓑ{I2}V2 →
- ∀J1,J2,W1,W2. L1.ⓑ{J1}W1 ≡[T, 1] L2.ⓑ{J2}W2.
-/2 width=5 by llpx_sn_bind_repl_SO/ qed-.