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/lsubd_da.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR DEGREE ASSIGNMENT ***********************)
19 (* Main properties **********************************************************)
21 theorem lsubd_trans: ∀h,g,G. Transitive … (lsubd h g G).
22 #h #g #G #L1 #L #H elim H -L1 -L
23 [ #X #H >(lsubd_inv_atom1 … H) -H //
24 | #I #L1 #L #Y #HL1 #IHL1 #X #H
25 elim (lsubd_inv_pair1 … H) -H * #L2
26 [ #HL2 #H destruct /3 width=1/
27 | #W #V #l #HV #HW #HL2 #H1 #H2 #H3 destruct
28 /3 width=3 by lsubd_beta, lsubd_da_trans/
30 | #L1 #L #W #V #l #HV #HW #HL1 #IHL1 #X #H
31 elim (lsubd_inv_pair1 … H) -H * #L2
32 [ #HL2 #H destruct /3 width=5 by lsubd_beta, lsubd_da_conf/
33 | #W0 #V0 #l0 #_ #_ #_ #H destruct