+(* Note: apparently this was missing in basic_1 *)
+lemma ldrop_trans_lt: ∀d1,e1,L1,L. ⇩[d1, e1] L1 ≡ L →
+ ∀e2,L2,I,V2. ⇩[0, e2] L ≡ L2.ⓑ{I}V2 →
+ e2 < d1 → let d ≝ d1 - e2 - 1 in
+ ∃∃L0,V0. ⇩[0, e2] L1 ≡ L0.ⓑ{I}V0 &
+ ⇩[d, e1] L0 ≡ L2 & ⇧[d, e1] V2 ≡ V0.
+#d1 #e1 #L1 #L #HL1 #e2 #L2 #I #V2 #HL2 #Hd21
+elim (ldrop_trans_le … HL1 … HL2) -L [2: /2 width=1/ ] #L0 #HL10 #HL02
+elim (ldrop_inv_skip2 … HL02) -HL02 [2: /2 width=1/ ] #L #V1 #HL2 #HV21 #H destruct /2 width=5/
+qed-.
+