include "basic_2/static/lsuba_aaa.ma".
-(* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
+(* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
(* Main properties **********************************************************)
-theorem lsuba_trans: ∀G,L1,L. G ⊢ L1 ⁝⊑ L → ∀L2. G ⊢ L ⁝⊑ L2 → G ⊢ L1 ⁝⊑ L2.
+theorem lsuba_trans: ∀G. Transitive … (lsuba G).
#G #L1 #L #H elim H -L1 -L
[ #X #H >(lsuba_inv_atom1 … H) -H //
-| #I #L1 #L #Y #HL1 #IHL1 #X #H
- elim (lsuba_inv_pair1 … H) -H * #L2
- [ #HL2 #H destruct /3 width=1/
- | #W #V #A #HV #HW #HL2 #H1 #H2 #H3 destruct
- /3 width=3 by lsuba_abbr, lsuba_aaa_trans/
+| #I #L1 #L #HL1 #IHL1 #Y #H
+ elim (lsuba_inv_bind1 … H) -H * #L2
+ [ #HL2 #H destruct /3 width=1 by lsuba_bind/
+ | #W #V #A #HV #HW #HL2 #H1 #H2 destruct
+ /3 width=3 by lsuba_beta, lsuba_aaa_trans/
]
-| #L1 #L #W #V #A #HV #HW #HL1 #IHL1 #X #H
- elim (lsuba_inv_pair1 … H) -H * #L2
- [ #HL2 #H destruct /3 width=5 by lsuba_abbr, lsuba_aaa_conf/
+| #L1 #L #W #V #A #HV #HW #HL1 #IHL1 #Y #H
+ elim (lsuba_inv_bind1 … H) -H * #L2
+ [ #HL2 #H destruct /3 width=5 by lsuba_beta, lsuba_aaa_conf/
| #W0 #V0 #A0 #_ #_ #_ #H destruct
]
]