/3 width=4 by lleq_sym, ex2_2_intro/
qed-.
-lemma lleq_inv_lref_ge: ∀L1,L2,d,i. L1 ⋕[#i, d] L2 → d ≤ i →
- ∀I1,I2,K1,K2,V.
- ⇩[i] L1 ≡ K1.ⓑ{I1}V → ⇩[i] L2 ≡ K2.ⓑ{I2}V → K1 ⋕[V, 0] K2.
-#L1 #L2 #d #i #HL12 #Hdi #I1 #I2 #K1 #K2 #V #HLK1 #HLK2
+lemma lleq_inv_lref_ge_gen: ∀L1,L2,d,i. L1 ⋕[#i, d] L2 → d ≤ i →
+ ∀I1,I2,K1,K2,V1,V2.
+ ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
+ V1 = V2 ∧ K1 ⋕[V2, 0] K2.
+#L1 #L2 #d #i #HL12 #Hdi #I1 #I2 #K1 #K2 #V1 #V2 #HLK1 #HLK2
elim (lleq_inv_lref_ge_sn … HL12 … HLK1) // -L1 -d
-#J #Y #HY lapply (ldrop_mono … HY … HLK2) -L2 -i #H destruct //
+#J #Y #HY lapply (ldrop_mono … HY … HLK2) -L2 -i #H destruct /2 width=1 by conj/
+qed-.
+
+lemma lleq_inv_lref_ge: ∀L1,L2,d,i. L1 ⋕[#i, d] L2 → d ≤ i →
+ ∀I,K1,K2,V. ⇩[i] L1 ≡ K1.ⓑ{I}V → ⇩[i] L2 ≡ K2.ⓑ{I}V →
+ K1 ⋕[V, 0] K2.
+#L1 #L2 #d #i #HL12 #Hdi #I #K1 #K2 #V #HLK1 #HLK2
+elim (lleq_inv_lref_ge_gen … HL12 … HLK1 HLK2) //
qed-.
(* Advanced properties ******************************************************)