milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / append / lpx.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/append/lpx.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/append/lpx.etc
new file mode 100644 (file)
index 0000000..a1976d5
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/append/lpx.etc
@@ -0,0 +1,13 @@
+lemma lpx_append: ∀h,g,G,K1,K2. ⦃G, K1⦄ ⊢ ➡[h, g] K2 → ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
+                  ⦃G, L1 @@ K1⦄ ⊢ ➡[h, g] L2 @@ K2.
+/3 width=1 by lpx_sn_append, cpx_append/ qed.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma lpx_fwd_append1: ∀h,g,G,K1,L1,L. ⦃G, K1 @@ L1⦄ ⊢ ➡[h, g] L →
+                       ∃∃K2,L2. ⦃G, K1⦄ ⊢ ➡[h, g] K2 & L = K2 @@ L2.
+/2 width=2 by lpx_sn_fwd_append1/ qed-.
+
+lemma lpx_fwd_append2: ∀h,g,G,L,K2,L2. ⦃G, L⦄ ⊢ ➡[h, g] K2 @@ L2 →
+                       ∃∃K1,L1. ⦃G, K1⦄ ⊢ ➡[h, g] K2 & L = K1 @@ L1.
+/2 width=2 by lpx_sn_fwd_append2/ qed-.