-lemma drop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
- ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
- ↓[0, e2 - e1] L1 ≡ L2.
+theorem drop_mono: ∀d,e,L,L1. ↓[d, e] L ≡ L1 →
+ ∀L2. ↓[d, e] L ≡ L2 → L1 = L2.
+#d #e #L #L1 #H elim H -H d e L L1
+[ #d #e #L2 #H
+ >(drop_inv_sort1 … H) -H L2 //
+| #K1 #K2 #I #V #HK12 #_ #L2 #HL12
+ <(drop_inv_refl … HK12) -HK12 K2
+ <(drop_inv_refl … HL12) -HL12 L2 //
+| #L #K #I #V #e #_ #IHLK #L2 #H
+ lapply (drop_inv_drop1 … H ?) -H /2/
+| #L #K1 #I #T #V1 #d #e #_ #HVT1 #IHLK1 #X #H
+ elim (drop_inv_skip1 … H ?) -H // <minus_plus_m_m #K2 #V2 #HLK2 #HVT2 #H destruct -X
+ >(lift_inj … HVT1 … HVT2) -HVT1 HVT2
+ >(IHLK1 … HLK2) -IHLK1 HLK2 //
+]
+qed.
+
+theorem drop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
+ ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
+ ↓[0, e2 - e1] L1 ≡ L2.