(* Properties with entrywise extension of context-sensitive relations *******)
-(* Basic_2A1: includes: lpx_sn_deliftable_dropable *) (**) (* changed after commit 13218 *)
+(**) (* changed after commit 13218 *)
lemma lexs_co_dropable_sn: ∀RN,RP. co_dropable_sn (lexs RN RP).
#RN #RP #b #f #L1 #K1 #H elim H -f -L1 -K1
[ #f #Hf #_ #f2 #X #H #f1 #Hf2 >(lexs_inv_atom1 … H) -X
]
qed-.
-(* Basic_2A1: includes: lpx_sn_liftable_dedropable *)
lemma lexs_liftable_co_dedropable_sn: ∀RN,RP. (∀L. reflexive … (RN L)) → (∀L. reflexive … (RP L)) →
d_liftable2_sn … liftsb RN → d_liftable2_sn … liftsb RP →
co_dedropable_sn (lexs RN RP).
]
qed-.
-(* Basic_2A1: includes: lpx_sn_dropable *)
lemma lexs_co_dropable_dx: ∀RN,RP. co_dropable_dx (lexs RN RP).
/2 width=5 by lexs_dropable_dx_aux/ qed-.
-(* Basic_2A1: includes: lpx_sn_drop_conf *) (**)
lemma lexs_drops_conf_next: ∀RN,RP.
∀f2,L1,L2. L1 ⪤*[RN, RP, f2] L2 →
∀b,f,I1,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I1} → 𝐔⦃f⦄ →
#I2 #K2 #HK12 #HI12 #H destruct /2 width=5 by ex3_2_intro/
qed-.
-(* Basic_2A1: includes: lpx_sn_drop_trans *)
lemma lexs_drops_trans_next: ∀RN,RP,f2,L1,L2. L1 ⪤*[RN, RP, f2] L2 →
∀b,f,I2,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I2} → 𝐔⦃f⦄ →
∀f1. f ~⊚ ↑f1 ≘ f2 →