include "basic_2/static/aaa_aaa.ma".
include "basic_2/static/lsuba.ma".
-(* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
+(* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
-(* Properties concerning atomic arity assignment ****************************)
+(* Properties with atomic arity assignment **********************************)
lemma lsuba_aaa_conf: ∀G,L1,V,A. ⦃G, L1⦄ ⊢ V ⁝ A →
∀L2. G ⊢ L1 ⫃⁝ 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_drop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
- elim (lsuba_inv_pair1 … H) -H * #K2
- [ #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 by aaa_lref/
- ]
+| #I #G #L1 #V #A #HA #IH #L2 #H
+ elim (lsuba_inv_pair1 … H) -H * /3 width=1 by aaa_zero/
+ #L0 #W0 #V0 #A0 #HV0 #HW0 #HL10 #H1 #H2 #H3 destruct
+ lapply (aaa_mono … HV0 … HA) #H destruct -V0 -L1 /2 width=1 by aaa_zero/
+| #I #G #K1 #V #A #i #_ #IH #L2 #H
+ elim (lsuba_inv_pair1 … H) -H * /3 width=1 by aaa_lref/
| /4 width=2 by lsuba_pair, aaa_abbr/
| /4 width=1 by lsuba_pair, aaa_abst/
| /3 width=3 by aaa_appl/
∀L1. G ⊢ L1 ⫃⁝ 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_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
- elim (lsuba_inv_pair2 … H) -H * #K1
- [ #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 by aaa_lref/
- ]
+| #I #G #L2 #V #A #HA #IH #L1 #H
+ elim (lsuba_inv_pair2 … H) -H * /3 width=1 by aaa_zero/
+ #L0 #V0 #A0 #HV0 #HV #HL02 #H1 #H2 destruct
+ lapply (aaa_mono … HV … HA) #H destruct -L2 /2 width=1 by aaa_zero/
+| #I #G #K2 #V #A #i #_ #IH #L1 #H
+ elim (lsuba_inv_pair2 … H) -H * /3 width=1 by aaa_lref/
| /4 width=2 by lsuba_pair, aaa_abbr/
| /4 width=1 by lsuba_pair, aaa_abst/
| /3 width=3 by aaa_appl/