(* *)
(**************************************************************************)
-include "basic_2/static/lsubss.ma".
+include "basic_2/equivalence/lsubss.ma".
(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED STATIC TYPE ASSIGNMENT *******)
#h #g #L1 #L2 #H elim H -L1 -L2
[ /2 width=3/
| #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
- elim (ldrop_inv_O1 … H) -H * #He #HLK1
+ elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
[ destruct
- elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
- <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
+ elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
+ <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
| elim (IHL12 … HLK1) -L1 /3 width=3/
]
-| #L1 #L2 #V #W #l #H1VW #H2VW #_ #IHL12 #K1 #e #H
- elim (ldrop_inv_O1 … H) -H * #He #HLK1
+| #L1 #L2 #V1 #V2 #W1 #W2 #l #HW12 #HVW1 #HWV2 #_ #IHL12 #K1 #e #H
+ elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
[ destruct
- elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
- <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
+ elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
+ <(ldrop_inv_O2 … H) in HL12; -H /3 width=6/
| elim (IHL12 … HLK1) -L1 /3 width=3/
]
]
-qed.
+qed-.
(* Note: the constant 0 cannot be generalized *)
lemma lsubss_ldrop_O1_trans: ∀h,g,L1,L2. h ⊢ L1 •⊑[g] L2 →
#h #g #L1 #L2 #H elim H -L1 -L2
[ /2 width=3/
| #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
- elim (ldrop_inv_O1 … H) -H * #He #HLK2
+ elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
[ destruct
- elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
- <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
+ elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
+ <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
| elim (IHL12 … HLK2) -L2 /3 width=3/
]
-| #L1 #L2 #V #W #l #H1VW #H2VW #_ #IHL12 #K2 #e #H
- elim (ldrop_inv_O1 … H) -H * #He #HLK2
+| #L1 #L2 #V1 #V2 #W1 #W2 #l #HW12 #HVW1 #HWV2 #_ #IHL12 #K2 #e #H
+ elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
[ destruct
- elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
- <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
+ elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
+ <(ldrop_inv_O2 … H) in HL12; -H /3 width=6/
| elim (IHL12 … HLK2) -L2 /3 width=3/
]
]
-qed.
+qed-.