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1 (**************************************************************************)
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3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
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10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
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14
15 include "static_2/static/lsuba_aaa.ma".
16
17 (* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
18
19 (* Main properties **********************************************************)
20
21 theorem lsuba_trans: ∀G. Transitive … (lsuba G).
22 #G #L1 #L #H elim H -L1 -L
23 [ #X #H >(lsuba_inv_atom1 … H) -H //
24 | #I #L1 #L #HL1 #IHL1 #Y #H
25   elim (lsuba_inv_bind1 … H) -H * #L2
26   [ #HL2 #H destruct /3 width=1 by lsuba_bind/
27   | #W #V #A #HV #HW #HL2 #H1 #H2 destruct
28     /3 width=3 by lsuba_beta, lsuba_aaa_trans/
29   ]
30 | #L1 #L #W #V #A #HV #HW #HL1 #IHL1 #Y #H
31   elim (lsuba_inv_bind1 … H) -H * #L2
32   [ #HL2 #H destruct /3 width=5 by lsuba_beta, lsuba_aaa_conf/
33   | #W0 #V0 #A0 #_ #_ #_ #H destruct
34   ]
35 ]
36 qed-.