(* Basic_1: was only: pr2_gen_cabbr *)
lemma thin_cpr_delift_conf: ∀L,U1,U2. L ⊢ U1 ➡ U2 →
- ∀K,d,e. L [d, e] ≡ K → ∀T1. L ⊢ U1 [d, e] ≡ T1 →
- ∃∃T2. K ⊢ T1 ➡ T2 & L ⊢ U2 [d, e] ≡ T2.
+ ∀K,d,e. ▼*[d, e] L ≡ K → ∀T1. L ⊢ ▼*[d, e] U1 ≡ T1 →
+ ∃∃T2. K ⊢ T1 ➡ T2 & L ⊢ ▼*[d, e] U2 ≡ T2.
#L #U1 #U2 * #U #HU1 #HU2 #K #d #e #HLK #T1 #HTU1
elim (tpr_delift_conf … HU1 … HTU1) -U1 #T #HT1 #HUT
elim (le_or_ge (|L|) d) #Hd