⇧[0, d] V2 ≡ U2 → L ⊢ ▼*[d, e] #i ≡ U2.
#L #K #V1 #V2 #U2 #i #d #e #Hdi #Hide #HLK * #V #HV1 #HV2 #HVU2
elim (lift_total V 0 (i+1)) #U #HVU
-lapply (lift_trans_be … HV2 … HVU ? ?) -HV2 // >minus_plus <plus_minus_m_m /2 width=1/ #HV2U
+lapply (lift_trans_be … HV2 … HVU ? ?) -HV2 // >minus_plus <plus_minus_m_m /2 width=1/ #HV2U
lapply (lift_conf_be … HVU2 … HV2U ?) //
>commutative_plus in ⊢ (??%??→?); <minus_plus_m_m /3 width=6/
qed.
qed-.
lemma delift_inv_lref1: ∀L,U2,i,d,e. L ⊢ ▼*[d, e] #i ≡ U2 →
- ∨∨ (i < d ∧ U2 = #i)
+ ∨∨ (i < d ∧ U2 = #i)
| (∃∃K,V1,V2. d ≤ i & i < d + e &
⇩[0, i] L ≡ K. ⓓV1 &
K ⊢ ▼*[0, d + e - i - 1] V1 ≡ V2 &