(* *)
(**************************************************************************)
-include "basic_2/unfold/lpqs.ma".
+include "basic_2/notation/relations/predsn_2.ma".
+include "basic_2/grammar/lpx_sn.ma".
include "basic_2/reduction/cpr.ma".
(* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
L1 @@ K1 ⊢ ➡ L2 @@ K2.
/3 width=1 by lpx_sn_append, cpr_append/ qed.
-lemma lpqs_lpr: ∀L1,L2. L1 ⊢ ➤* L2 → L1 ⊢ ➡ L2.
-#L1 #L2 #H elim H -L1 -L2 // /3 width=1/
-qed.
-
-lemma lpss_lpr: ∀L1,L2. L1 ⊢ ▶* L2 → L1 ⊢ ➡ L2.
-/3 width=1/ qed.
-
(* Basic forward lemmas *****************************************************)
lemma lpr_fwd_length: ∀L1,L2. L1 ⊢ ➡ L2 → |L1| = |L2|.