(* Properties with degree-based equivalence for terms ***********************)
-lemma tdeq_lifts: ∀h,o. liftable2 (tdeq h o).
+lemma tdeq_lifts_sn: ∀h,o. liftable2_sn (tdeq h o).
#h #o #T1 #T2 #H elim H -T1 -T2 [||| * ]
[ #s1 #s2 #d #Hs1 #Hs2 #f #X #H >(lifts_inv_sort1 … H) -H
/3 width=5 by lifts_sort, tdeq_sort, ex2_intro/
qed-.
lemma tdeq_lifts_bi: ∀h,o. liftable2_bi (tdeq h o).
-/3 width=6 by tdeq_lifts, liftable2_sn_bi/ qed-.
+/3 width=6 by tdeq_lifts_sn, liftable2_sn_bi/ qed-.
(* Inversion lemmas with degree-based equivalence for terms *****************)
-lemma tdeq_inv_lifts: ∀h,o. deliftable2_sn (tdeq h o).
+lemma tdeq_inv_lifts_sn: ∀h,o. deliftable2_sn (tdeq h o).
#h #o #U1 #U2 #H elim H -U1 -U2 [||| * ]
[ #s1 #s2 #d #Hs1 #Hs2 #f #X #H >(lifts_inv_sort2 … H) -H
/3 width=5 by lifts_sort, tdeq_sort, ex2_intro/
qed-.
lemma tdeq_inv_lifts_bi: ∀h,o. deliftable2_bi (tdeq h o).
-/3 width=6 by tdeq_inv_lifts, deliftable2_sn_bi/ qed-.
+/3 width=6 by tdeq_inv_lifts_sn, deliftable2_sn_bi/ qed-.