-lemma cpr_inv_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
- ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ➡ U2 →
- ∃∃T2. ⇧[d, e] T2 ≡ U2 & K ⊢ T1 ➡ T2.
+lemma cpr_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+ ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ➡ U2 →
+ ∃∃T2. ⇧[d, e] T2 ≡ U2 & K ⊢ T1 ➡ T2.