⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ K2.ⓑ{I}V2.
/2 width=1/ qed.
-lemma lpr_append: ∀G,K1,K2. ⦃G, K1⦄ ⊢ ➡ K2 → ∀L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 →
- ⦃G, L1 @@ K1⦄ ⊢ ➡ L2 @@ K2.
-/3 width=1 by lpx_sn_append, cpr_append/ qed.
-
(* Basic forward lemmas *****************************************************)
lemma lpr_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → |L1| = |L2|.
/2 width=2 by lpx_sn_fwd_length/ qed-.
-(* Advanced forward lemmas **************************************************)
-
-lemma lpr_fwd_append1: ∀G,K1,L1,L. ⦃G, K1 @@ L1⦄ ⊢ ➡ L →
- ∃∃K2,L2. ⦃G, K1⦄ ⊢ ➡ K2 & L = K2 @@ L2.
-/2 width=2 by lpx_sn_fwd_append1/ qed-.
-
-lemma lpr_fwd_append2: ∀G,L,K2,L2. ⦃G, L⦄ ⊢ ➡ K2 @@ L2 →
- ∃∃K1,L1. ⦃G, K1⦄ ⊢ ➡ K2 & L = K1 @@ L1.
-/2 width=2 by lpx_sn_fwd_append2/ qed-.
-
(* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back
pr0_subst1_back
*)