+
+lemma delift_inv_lift1_eq: ∀L,U1,T2,d,e. L ⊢ U1 ▼*[d, e] ≡ T2 →
+ ∀K. ⇩[d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 → T1 = T2.
+#L #U1 #T2 #d #e * #U2 #HU12 #HTU2 #K #HLK #T1 #HTU1
+lapply (tpss_inv_lift1_eq … HU12 … HTU1) -L -K #H destruct
+lapply (lift_inj … HTU1 … HTU2) -U2 //
+qed-.
+
+lemma delift_lift_div_be: ∀L,T1,T,d,e,i. L ⊢ T1 ▼*[i, d + e - i] ≡ T →
+ ∀T2. ⇧[d, i - d] T2 ≡ T → d ≤ i → i ≤ d + e →
+ L ⊢ T1 ▼*[d, e] ≡ T2.
+#L #T1 #T #d #e #i * #T0 #HT10 #HT0 #T2 #HT2 #Hdi #Hide
+lapply (tpss_weak … HT10 d e ? ?) -HT10 // [ >commutative_plus /2 width=1/ ] #HT10
+lapply (lift_trans_be … HT2 … HT0 ? ?) -T //
+>commutative_plus >commutative_plus in ⊢ (? ? (? % ?) ? ? → ?);
+<minus_le_minus_minus_comm // <plus_minus_m_m [ /2 width=3/ | /2 width=1/ ]
+qed.