@lexs_co_dropable_dx qed-.
(* Basic_2A1: includes: lreq_drop_trans_be *)
-lemma lreq_drops_trans_next: â\88\80f2,L1,L2. L1 â\89¡[f2] L2 →
+lemma lreq_drops_trans_next: â\88\80f2,L1,L2. L1 â\89\90[f2] L2 →
∀b,f,I,K2. ⬇*[b, f] L2 ≡ K2.ⓘ{I} → 𝐔⦃f⦄ →
∀f1. f ~⊚ ⫯f1 ≡ f2 →
- â\88\83â\88\83K1. â¬\87*[b, f] L1 â\89¡ K1.â\93\98{I} & K1 â\89¡[f1] K2.
+ â\88\83â\88\83K1. â¬\87*[b, f] L1 â\89¡ K1.â\93\98{I} & K1 â\89\90[f1] K2.
#f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
elim (lexs_drops_trans_next … HL12 … HLK2 Hf … Hf2) -f2 -L2 -Hf
#I1 #K1 #HLK1 #HK12 #H <(ceq_ext_inv_eq … H) -I2
qed-.
(* Basic_2A1: includes: lreq_drop_conf_be *)
-lemma lreq_drops_conf_next: â\88\80f2,L1,L2. L1 â\89¡[f2] L2 →
+lemma lreq_drops_conf_next: â\88\80f2,L1,L2. L1 â\89\90[f2] L2 →
∀b,f,I,K1. ⬇*[b, f] L1 ≡ K1.ⓘ{I} → 𝐔⦃f⦄ →
∀f1. f ~⊚ ⫯f1 ≡ f2 →
- â\88\83â\88\83K2. â¬\87*[b, f] L2 â\89¡ K2.â\93\98{I} & K1 â\89¡[f1] K2.
+ â\88\83â\88\83K2. â¬\87*[b, f] L2 â\89¡ K2.â\93\98{I} & K1 â\89\90[f1] K2.
#f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
elim (lreq_drops_trans_next … (lreq_sym … HL12) … HLK1 … Hf2) // -f2 -L1 -Hf
/3 width=3 by lreq_sym, ex2_intro/
qed-.
-lemma drops_lreq_trans_next: â\88\80f1,K1,K2. K1 â\89¡[f1] K2 →
+lemma drops_lreq_trans_next: â\88\80f1,K1,K2. K1 â\89\90[f1] K2 →
∀b,f,I,L1. ⬇*[b, f] L1.ⓘ{I} ≡ K1 →
∀f2. f ~⊚ f1 ≡ ⫯f2 →
- â\88\83â\88\83L2. â¬\87*[b, f] L2.â\93\98{I} â\89¡ K2 & L1 â\89¡[f2] L2 & L1.â\93\98{I} â\89¡[f] L2.ⓘ{I}.
+ â\88\83â\88\83L2. â¬\87*[b, f] L2.â\93\98{I} â\89¡ K2 & L1 â\89\90[f2] L2 & L1.â\93\98{I} â\89\90[f] L2.ⓘ{I}.
#f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
elim (drops_lexs_trans_next … HK12 … HLK1 … Hf2) -f1 -K1
/2 width=6 by cfull_lift_sn, ceq_lift_sn/