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/dynamic/snv_aaa.ma".
16 include "basic_2/dynamic/lsubsv.ma".
18 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
20 (* Properties on local environment refinement for atomic arity assignment ***)
22 lemma lsubsv_fwd_lsuba: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ⁝⊑ L2.
23 #h #g #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
24 #L1 #L2 #V1 #V2 #W1 #W2 #l #HV1 #HVW1 #HW12 #HW2 #_ #_ #HL12
25 elim (snv_fwd_aaa … HV1) -HV1 #A #HV1
26 elim (snv_fwd_aaa … HW2) -HW2 #B #HW2
27 lapply (ssta_aaa … HV1 … HVW1) -HVW1 #H1
28 lapply (lsuba_aaa_trans … HW2 … HL12) #H2
29 lapply (aaa_cpcs_mono … HW12 … H1 … H2) -W1 -H2 #H destruct /2 width=3/