- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / append / crx_append.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/crx_append.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/crx_append.etc
new file mode 100644 (file)
index 0000000..56667b2
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/crx_append.etc
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/relocation/ldrop_append.ma".
+include "basic_2/reduction/crx.ma".
+
+(* REDUCIBLE TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION *****************)
+
+(* Advanved properties ******************************************************)
+
+lemma crx_append_sn: ∀h,g,G,L,K,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄  → ⦃G, K @@ L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄.
+#h #g #G #L #K0 #T #H elim H -L -T
+/2 width=2 by crx_sort, crx_appl_sn, crx_appl_dx, crx_ri2, crx_ib2_sn, crx_ib2_dx, crx_beta, crx_theta/
+#I #L #K #V #i #HLK
+lapply (ldrop_fwd_length_lt2 … HLK) #Hi
+lapply (ldrop_O1_append_sn_le … HLK … K0) -HLK /2 width=4 by crx_delta, lt_to_le/
+qed.
+
+lemma trx_crx: ∀h,g,G,L,T. ⦃G, ⋆⦄ ⊢ ➡[h, g] 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄.
+#h #g #G #L #T #H lapply (crx_append_sn … H) //
+qed.