(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
(* Basic_2A1: includes: lsuba_drop_O1_trans *)
-lemma lsuba_drop_O1_trans: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 →
- ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≡ K2 →
- ∃∃K1. G ⊢ K1 ⫃⁝ K2 & ⬇*[b, f] L1 ≡ K1.
+lemma lsuba_drops_trans_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 →
+ ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≡ K2 →
+ ∃∃K1. G ⊢ K1 ⫃⁝ K2 & ⬇*[b, f] L1 ≡ K1.
#G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #V #HL12 #IH #b #f #K2 #Hf #H