(* *)
(**************************************************************************)
+include "basic_2/notation/relations/predsn_4.ma".
include "basic_2/reduction/lpr.ma".
include "basic_2/reduction/cpx.ma".
lemma lpx_append: ∀h,g,K1,K2. ⦃h, K1⦄ ⊢ ➡[g] K2 → ∀L1,L2. ⦃h, L1⦄ ⊢ ➡[g] L2 →
⦃h, L1 @@ K1⦄ ⊢ ➡[g] L2 @@ K2.
/3 width=1 by lpx_sn_append, cpx_append/ qed.
-(*
-lamma lpr_lpx: ∀h,g,L1,L2. L1 ⊢ ➡ L2 → ⦃h, L1⦄ ⊢ ➡[g] L2.
+
+lemma lpr_lpx: ∀h,g,L1,L2. L1 ⊢ ➡ L2 → ⦃h, L1⦄ ⊢ ➡[g] L2.
#h #g #L1 #L2 #H elim H -L1 -L2 // /3 width=1/
qed.
-*)
+
(* Basic forward lemmas *****************************************************)
lemma lpx_fwd_length: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡[g] L2 → |L1| = |L2|.