(* Properties on degree assignment ******************************************)
-lemma lsubd_da_trans: ∀h,g,G,L2,T,l. ⦃G, L2⦄ ⊢ T ▪[h, g] l →
- ∀L1. G ⊢ L1 ⫃▪[h, g] L2 → ⦃G, L1⦄ ⊢ T ▪[h, g] l.
-#h #g #G #L2 #T #l #H elim H -G -L2 -T -l
+lemma lsubd_da_trans: ∀h,g,G,L2,T,d. ⦃G, L2⦄ ⊢ T ▪[h, g] d →
+ ∀L1. G ⊢ L1 ⫃▪[h, g] L2 → ⦃G, L1⦄ ⊢ T ▪[h, g] d.
+#h #g #G #L2 #T #d #H elim H -G -L2 -T -d
[ /2 width=1/
-| #G #L2 #K2 #V #i #l #HLK2 #_ #IHV #L1 #HL12
+| #G #L2 #K2 #V #i #d #HLK2 #_ #IHV #L1 #HL12
elim (lsubd_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
elim (lsubd_inv_pair2 … H) -H * #K1 [ | -IHV -HLK1 ]
[ #HK12 #H destruct /3 width=4/
- | #W #l0 #_ #_ #_ #H destruct
+ | #W #d0 #_ #_ #_ #H destruct
]
-| #G #L2 #K2 #W #i #l #HLK2 #HW #IHW #L1 #HL12
+| #G #L2 #K2 #W #i #d #HLK2 #HW #IHW #L1 #HL12
elim (lsubd_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
elim (lsubd_inv_pair2 … H) -H * #K1 [ -HW | -IHW ]
[ #HK12 #H destruct /3 width=4/
- | #V #l0 #HV #H0W #_ #_ #H destruct
+ | #V #d0 #HV #H0W #_ #_ #H destruct
lapply (da_mono … H0W … HW) -H0W -HW #H destruct /3 width=7/
]
| /4 width=1/
]
qed-.
-lemma lsubd_da_conf: ∀h,g,G,L1,T,l. ⦃G, L1⦄ ⊢ T ▪[h, g] l →
- ∀L2. G ⊢ L1 ⫃▪[h, g] L2 → ⦃G, L2⦄ ⊢ T ▪[h, g] l.
-#h #g #G #L1 #T #l #H elim H -G -L1 -T -l
+lemma lsubd_da_conf: ∀h,g,G,L1,T,d. ⦃G, L1⦄ ⊢ T ▪[h, g] d →
+ ∀L2. G ⊢ L1 ⫃▪[h, g] L2 → ⦃G, L2⦄ ⊢ T ▪[h, g] d.
+#h #g #G #L1 #T #d #H elim H -G -L1 -T -d
[ /2 width=1/
-| #G #L1 #K1 #V #i #l #HLK1 #HV #IHV #L2 #HL12
+| #G #L1 #K1 #V #i #d #HLK1 #HV #IHV #L2 #HL12
elim (lsubd_drop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
elim (lsubd_inv_pair1 … H) -H * #K2 [ -HV | -IHV ]
[ #HK12 #H destruct /3 width=4/
- | #W0 #V0 #l0 #HV0 #HW0 #_ #_ #H1 #H2 destruct
+ | #W0 #V0 #d0 #HV0 #HW0 #_ #_ #H1 #H2 destruct
lapply (da_inv_flat … HV) -HV #H0V0
lapply (da_mono … H0V0 … HV0) -H0V0 -HV0 #H destruct /2 width=4/
]
-| #G #L1 #K1 #W #i #l #HLK1 #HW #IHW #L2 #HL12
+| #G #L1 #K1 #W #i #d #HLK1 #HW #IHW #L2 #HL12
elim (lsubd_drop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
elim (lsubd_inv_pair1 … H) -H * #K2 [ -HW | -IHW ]
[ #HK12 #H destruct /3 width=4/
- | #W0 #V0 #l0 #HV0 #HW0 #_ #H destruct
+ | #W0 #V0 #d0 #HV0 #HW0 #_ #H destruct
]
| /4 width=1/
| /3 width=1/