(* Properties with generic slicing for local environments *******************)
(* Basic_2A1: includes: cpx_lift *)
-lemma cpx_lifts_sn: ∀h,G. d_liftable2_sn (cpx h G).
+lemma cpx_lifts_sn: ∀h,G. d_liftable2_sn … lifts (cpx h G).
#h #G #K #T1 #T2 * #cT #HT12 #b #f #L #HLK #U1 #HTU1
elim (cpg_lifts_sn … HT12 … HLK … HTU1) -K -T1
/3 width=4 by ex2_intro, ex_intro/
qed-.
-lemma cpx_lifts_bi: ∀h,G. d_liftable2_bi (cpx h G).
-/3 width=9 by cpx_lifts_sn, d_liftable2_sn_bi/ qed-.
+lemma cpx_lifts_bi: ∀h,G. d_liftable2_bi … lifts (cpx h G).
+#h #G #K #T1 #T2 * /3 width=10 by cpg_lifts_bi, ex_intro/
+qed-.
(* Inversion lemmas with generic slicing for local environments *************)
(* Basic_2A1: includes: cpx_inv_lift1 *)
-lemma cpx_inv_lifts_sn: ∀h,G. d_deliftable2_sn (cpx h G).
+lemma cpx_inv_lifts_sn: ∀h,G. d_deliftable2_sn … lifts (cpx h G).
#h #G #L #U1 #U2 * #cU #HU12 #b #f #K #HLK #T1 #HTU1
elim (cpg_inv_lifts_sn … HU12 … HLK … HTU1) -L -U1
/3 width=4 by ex2_intro, ex_intro/
qed-.
-lemma cpx_inv_lifts_bi: ∀h,G. d_deliftable2_bi (cpx h G).
-/3 width=9 by cpx_inv_lifts_sn, d_deliftable2_sn_bi/ qed-.
+lemma cpx_inv_lifts_bi: ∀h,G. d_deliftable2_bi …lifts (cpx h G).
+#h #G #L #U1 #U2 * /3 width=10 by cpg_inv_lifts_bi, ex_intro/
+qed-.