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 *)
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15 include "basic_2/static/lsuba_aaa.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
19 (* Main properties **********************************************************)
21 theorem lsuba_trans: ∀L1,L. L1 ÷⊑ L → ∀L2. L ÷⊑ L2 → L1 ÷⊑ L2.
22 #L1 #L #H elim H -L1 -L
23 [ #X #H >(lsuba_inv_atom1 … H) -H //
24 | #I #L1 #L #V #HL1 #IHL1 #X #H
25 elim (lsuba_inv_pair1 … H) -H * #L2
26 [ #HL2 #H destruct /3 width=1/
27 | #V #A #HLV #HL2V #HL2 #H1 #H2 destruct /3 width=3/
29 | #L1 #L #V1 #W #A1 #HV1 #HW #HL1 #IHL1 #X #H
30 elim (lsuba_inv_pair1 … H) -H * #L2
31 [ #HL2 #H destruct /3 width=5/
32 | #V #A2 #_ #_ #_ #_ #H destruct