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/static/lsubss_ssta.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR STATIC TYPE ASSIGNMENT ******************)
19 (* Main properties **********************************************************)
21 theorem lsubss_trans: ∀h,g,L1,L. h ⊢ L1 •⊑[g] L → ∀L2. h ⊢ L •⊑[g] L2 →
23 #h #g #L1 #L #H elim H -L1 -L
24 [ #X #H >(lsubss_inv_atom1 … H) -H //
25 | #I #L1 #L #W #HL1 #IHL1 #X #H
26 elim (lsubss_inv_pair1 … H) -H * #L2
27 [ #HL2 #H destruct /3 width=1/
28 | #V #l #H1WV #H2WV #HL2 #H1 #H2 destruct /3 width=3/
30 | #L1 #L #V1 #W1 #l #H1VW1 #H2VW1 #HL1 #IHL1 #X #H
31 elim (lsubss_inv_pair1 … H) -H * #L2
32 [ #HL2 #H destruct /3 width=5/
33 | #V #l0 #_ #_ #_ #_ #H destruct