(* Basic_2A1: uses: llpx_sn_lift_le llpx_sn_lift_ge *)
lemma lfxs_lifts_bi: ∀R.d_liftable2_sn … lifts R →
∀L1,L2. |L1| = |L2| → ∀K1,K2,T. K1 ⪤*[R, T] K2 →
- â\88\80b,f. â¬\87*[b, f] L1 â\89¡ K1 â\86\92 â¬\87*[b, f] L2 â\89¡ K2 →
- â\88\80U. â¬\86*[f] T â\89¡ U → L1 ⪤*[R, U] L2.
+ â\88\80b,f. â¬\87*[b, f] L1 â\89\98 K1 â\86\92 â¬\87*[b, f] L2 â\89\98 K2 →
+ â\88\80U. â¬\86*[f] T â\89\98 U → L1 ⪤*[R, U] L2.
#R #HR #L1 #L2 #HL12 #K1 #K2 #T * #f1 #Hf1 #HK12 #b #f #HLK1 #HLK2 #U #HTU
elim (frees_total L1 U) #f2 #Hf2
lapply (frees_fwd_coafter … Hf2 … HLK1 … HTU … Hf1) -HTU #Hf