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/computation/lsubc_ldrop.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
19 (* Properties concerning generic local environment slicing ******************)
21 (* Basic_1: was: csubc_drop1_conf_rev *)
22 lemma ldrops_lsubc_trans: ∀RR,RS,RP.
23 acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
24 ∀G,L1,K1,des. ⇩*[Ⓕ, des] L1 ≡ K1 → ∀K2. G ⊢ K1 ⊑[RP] K2 →
25 ∃∃L2. G ⊢ L1 ⊑[RP] L2 & ⇩*[Ⓕ, des] L2 ≡ K2.
26 #RR #RS #RP #Hacp #Hacr #G #L1 #K1 #des #H elim H -L1 -K1 -des
27 [ /2 width=3 by ldrops_nil, ex2_intro/
28 | #L1 #L #K1 #des #d #e #_ #HLK1 #IHL #K2 #HK12
29 elim (ldrop_lsubc_trans … Hacp Hacr … HLK1 … HK12) -Hacp -Hacr -K1 #K #HLK #HK2
30 elim (IHL … HLK) -IHL -HLK /3 width=5 by ldrops_cons, ex2_intro/