include "basic_2/relocation/drops_ceq.ma".
include "basic_2/relocation/drops_lexs.ma".
-include "basic_2/static/frees_fqup.ma".
include "basic_2/static/frees_drops.ma".
include "basic_2/static/lfxs.ma".
(* Properties with generic slicing for local environments *******************)
(* Basic_2A1: includes: llpx_sn_lift_le llpx_sn_lift_ge *)
-lemma lfxs_liftable_dedropable: ∀R. (∀L. reflexive ? (R L)) →
- d_liftable2 R → dedropable_sn R.
+lemma lfxs_liftable_dedropable_sn: ∀R. (∀L. reflexive ? (R L)) →
+ d_liftable2_sn R → dedropable_sn R.
#R #H1R #H2R #b #f #L1 #K1 #HLK1 #K2 #T * #f1 #Hf1 #HK12 #U #HTU
elim (frees_total L1 U) #f2 #Hf2
lapply (frees_fwd_coafter … Hf2 … HLK1 … HTU … Hf1) -HTU #Hf
-elim (lexs_liftable_co_dedropable … H1R … H2R … HLK1 … HK12 … Hf) -f1 -K1
-/3 width=6 by cfull_lift, ex3_intro, ex2_intro/
+elim (lexs_liftable_co_dedropable_sn … H1R … H2R … HLK1 … HK12 … Hf) -f1 -K1
+/3 width=6 by cfull_lift_sn, ex3_intro, ex2_intro/
qed-.
(* Inversion lemmas with generic slicing for local environments *************)
qed-.
(* Basic_2A1: was: llpx_sn_inv_lift_O *)
-lemma lfxs_inv_lift_bi: ∀R,L1,L2,U. L1 ⦻*[R, U] L2 →
- ∀K1,K2,i. ⬇*[i] L1 ≡ K1 → ⬇*[i] L2 ≡ K2 →
- ∀T. ⬆*[i] T ≡ U → K1 ⦻*[R, T] K2.
+lemma lfxs_inv_lifts_bi: ∀R,L1,L2,U. L1 ⦻*[R, U] L2 →
+ ∀K1,K2,i. ⬇*[i] L1 ≡ K1 → ⬇*[i] L2 ≡ K2 →
+ ∀T. ⬆*[i] T ≡ U → K1 ⦻*[R, T] K2.
#R #L1 #L2 #U #HL12 #K1 #K2 #i #HLK1 #HLK2 #T #HTU
elim (lfxs_dropable_sn … HLK1 … HL12 … HTU) -L1 -U // #Y #HK12 #HY
lapply (drops_mono … HY … HLK2) -L2 -i #H destruct //