(* *)
(**************************************************************************)
-include "basic_2/syntax/lveq_length.ma".
include "basic_2/relocation/lifts_tdeq.ma".
include "basic_2/static/lfxs_length.ma".
include "basic_2/static/lfxs_fsle.ma".
(* Advanved properties with free variables inclusion ************************)
-lemma lfdeq_fsle_comp: ∀h,o. lfxs_fsle_compatible (cdeq h o).
+lemma lfdeq_fsge_comp (h) (o): lfxs_fsge_compatible (cdeq h o).
#h #o #L1 #L2 #T * #f1 #Hf1 #HL12
lapply (frees_lfdeq_conf h o … Hf1 … HL12)
lapply (lexs_fwd_length … HL12)
(* Properties with length for local environments ****************************)
+(* Basic_2A1: uses: lleq_sort *)
+lemma lfdeq_sort_length (h) (o): ∀L1,L2. |L1| = |L2| → ∀s. L1 ≛[h, o, ⋆s] L2.
+/2 width=1 by lfxs_sort_length/ qed.
+
+(* Basic_2A1: uses: lleq_gref *)
+lemma lfdeq_gref_length (h) (o): ∀L1,L2. |L1| = |L2| → ∀l. L1 ≛[h, o, §l] L2.
+/2 width=1 by lfxs_gref_length/ qed.
+
+lemma lfdeq_unit_length (h) (o): ∀L1,L2. |L1| = |L2| →
+ ∀I. L1.ⓤ{I} ≛[h, o, #0] L2.ⓤ{I}.
+/2 width=1 by lfxs_unit_length/ qed.
+
(* Basic_2A1: uses: lleq_lift_le lleq_lift_ge *)
-lemma lfdeq_lifts_bi: ∀L1,L2. |L1| = |L2| → ∀h,o,K1,K2,T. K1 ≛[h, o, T] K2 →
- ∀b,f. ⬇*[b, f] L1 ≡ K1 → ⬇*[b, f] L2 ≡ K2 →
- ∀U. ⬆*[f] T ≡ U → L1 ≛[h, o, U] L2.
+lemma lfdeq_lifts_bi (h) (o): ∀L1,L2. |L1| = |L2| → ∀K1,K2,T. K1 ≛[h, o, T] K2 →
+ ∀b,f. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
+ ∀U. ⬆*[f] T ≘ U → L1 ≛[h, o, U] L2.
/3 width=9 by lfxs_lifts_bi, tdeq_lifts_sn/ qed-.
(* Forward lemmas with length for local environments ************************)
(* Basic_2A1: lleq_fwd_length *)
-lemma lfdeq_fwd_length: ∀h,o,L1,L2. ∀T:term. L1 ≛[h, o, T] L2 → |L1| = |L2|.
+lemma lfdeq_fwd_length (h) (o): ∀L1,L2. ∀T:term. L1 ≛[h, o, T] L2 → |L1| = |L2|.
/2 width=3 by lfxs_fwd_length/ qed-.
-