(* Properties on append for local environments ******************************)
-fact ldrop_O1_append_sn_le_aux: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 →
+fact ldrop_O1_append_sn_le_aux: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 →
d = 0 → e ≤ |L1| →
∀L. ⇩[0, e] L @@ L1 ≡ L @@ L2.
#L1 #L2 #d #e #H elim H -L1 -L2 -d -e normalize // /4 width=1/
[ #H1 #_ #K2 #H2
lapply (ldrop_inv_refl … H1) -H1 #H1
lapply (ldrop_inv_refl … H2) -H2 #H2 destruct //
- | #e #_ #H1 #H1e #K2 #H2
+ | #e #_ #H1 #H #K2 #H2
+ lapply (le_plus_to_le_r … H) -H
lapply (ldrop_inv_ldrop1 … H1 ?) -H1 //
- lapply (ldrop_inv_ldrop1 … H2 ?) -H2 // /3 width=4/
+ lapply (ldrop_inv_ldrop1 … H2 ?) -H2 //
+ <minus_plus_m_m /2 width=4/
]
]
-qed-.
+qed-.