1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/substitution/llor.ma".
16 include "basic_2/substitution/lleq_alt.ma".
18 (* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
20 (* Properties on poinwise union for local environments **********************)
22 lemma llpx_sn_llor_dx: āR,L1,L2.
23 (āU,i. L2 ā¢ i Ļµ š
*[0]ā¦Uā¦ ā L1 ā¢ i Ļµ š
*[0]ā¦Uā¦) ā
24 āT. llpx_sn R 0 T L1 L2 ā āL. L1 ā©[T] L2 ā” L ā L2 ā”[T, 0] L.
25 #R #L1 #L2 #HR #T #H1 #L #H2
26 elim (llpx_sn_llpx_sn_alt ā¦ H1) -H1 #HL12 #IH1
27 elim H2 -H2 #_ #HL1 #IH2
28 @lleq_intro_alt // #I2 #I #K2 #K #V2 #V #i #Hi #HnT #HLK2 #HLK
29 lapply (ldrop_fwd_length_lt2 ā¦ HLK) #HiL
30 elim (ldrop_O1_lt (ā») L1 i) // -HiL #I1 #K1 #V1 #HLK1
31 elim (IH1 ā¦ HLK1 HLK2) -IH1 /2 width=1 by/ #H #_ destruct
32 elim (IH2 ā¦ HLK1 HLK2 HLK) -IH2 -HLK1 -HLK2 -HLK * /2 width=1 by conj/ #H
33 elim H -H /2 width=1 by/