(**************************************************************************)
include "basic_2/static/aaa_aaa.ma".
-include "basic_2/static/lsuba_ldrop.ma".
+include "basic_2/static/lsuba.ma".
(* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
(* Properties concerning atomic arity assignment ****************************)
lemma lsuba_aaa_conf: ∀G,L1,V,A. ⦃G, L1⦄ ⊢ V ⁝ A →
- â\88\80L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ⦃G, L2⦄ ⊢ V ⁝ A.
+ â\88\80L2. G â\8a¢ L1 â«\83â\81\9d L2 → ⦃G, L2⦄ ⊢ V ⁝ A.
#G #L1 #V #A #H elim H -G -L1 -V -A
[ //
| #I #G #L1 #K1 #V #A #i #HLK1 #HV #IHV #L2 #HL12
- elim (lsuba_ldrop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
+ elim (lsuba_drop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
elim (lsuba_inv_pair1 … H) -H * #K2
- [ #HK12 #H destruct /3 width=5/
+ [ #HK12 #H destruct /3 width=5 by aaa_lref/
| #W0 #V0 #A0 #HV0 #HW0 #_ #H1 #H2 #H3 destruct
- lapply (aaa_mono … HV0 … HV) #H destruct -V0 /2 width=5/
+ lapply (aaa_mono … HV0 … HV) #H destruct -V0 /2 width=5 by aaa_lref/
]
-| /4 width=2/
-| /4 width=1/
-| /3 width=3/
-| /3 width=1/
+| /4 width=2 by lsuba_pair, aaa_abbr/
+| /4 width=1 by lsuba_pair, aaa_abst/
+| /3 width=3 by aaa_appl/
+| /3 width=1 by aaa_cast/
]
qed-.
lemma lsuba_aaa_trans: ∀G,L2,V,A. ⦃G, L2⦄ ⊢ V ⁝ A →
- â\88\80L1. G â\8a¢ L1 â\81\9dâ«\83 L2 → ⦃G, L1⦄ ⊢ V ⁝ A.
+ â\88\80L1. G â\8a¢ L1 â«\83â\81\9d L2 → ⦃G, L1⦄ ⊢ V ⁝ A.
#G #L2 #V #A #H elim H -G -L2 -V -A
[ //
| #I #G #L2 #K2 #V #A #i #HLK2 #H1V #IHV #L1 #HL12
- elim (lsuba_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+ elim (lsuba_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
elim (lsuba_inv_pair2 … H) -H * #K1
- [ #HK12 #H destruct /3 width=5/
+ [ #HK12 #H destruct /3 width=5 by aaa_lref/
| #V0 #A0 #HV0 #H2V #_ #H1 #H2 destruct
- lapply (aaa_mono … H2V … H1V) #H destruct -K2 /2 width=5/
+ lapply (aaa_mono … H2V … H1V) #H destruct -K2 /2 width=5 by aaa_lref/
]
-| /4 width=2/
-| /4 width=1/
-| /3 width=3/
-| /3 width=1/
+| /4 width=2 by lsuba_pair, aaa_abbr/
+| /4 width=1 by lsuba_pair, aaa_abst/
+| /3 width=3 by aaa_appl/
+| /3 width=1 by aaa_cast/
]
qed-.