(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
(* Basic_2A1: includes: lsuba_drop_O1_conf *)
lemma lsuba_drops_conf_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 →
- â\88\80b,f,K1. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â¬\87*[b, f] L1 ≘ K1 →
- â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & â¬\87*[b, f] L2 ≘ K2.
+ â\88\80b,f,K1. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\87©*[b,f] L1 ≘ K1 →
+ â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & â\87©*[b,f] L2 ≘ K2.
#G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #HL12 #IH #b #f #K1 #Hf #H
(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
(* Basic_2A1: includes: lsuba_drop_O1_trans *)
lemma lsuba_drops_trans_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 →
- â\88\80b,f,K2. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â¬\87*[b, f] L2 ≘ K2 →
- â\88\83â\88\83K1. G â\8a¢ K1 â«\83â\81\9d K2 & â¬\87*[b, f] L1 ≘ K1.
+ â\88\80b,f,K2. ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\87©*[b,f] L2 ≘ K2 →
+ â\88\83â\88\83K1. G â\8a¢ K1 â«\83â\81\9d K2 & â\87©*[b,f] L1 ≘ K1.
#G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H