-theorem ldrops_trans: ∀L,L2,des2. ⇩*[des2] L ≡ L2 → ∀L1,des1. ⇩*[des1] L1 ≡ L →
- ⇩*[des2 @@ des1] L1 ≡ L2.
-#L #L2 #des2 #H elim H -L -L2 -des2 // /3 width=3/
-qed.
+theorem ldrops_trans: ∀L,L2,s,des2. ⇩*[s, des2] L ≡ L2 → ∀L1,des1. ⇩*[s, des1] L1 ≡ L →
+ ⇩*[s, des2 @@ des1] L1 ≡ L2.
+#L #L2 #s #des2 #H elim H -L -L2 -des2 /3 width=3 by ldrops_cons/
+qed-.