- lambda_delta: programmed renaming to lambdadelta

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / etc / lenv_px / lenv_px_sn.etc

diff --git a/matita/matita/contribs/lambda_delta/basic_2/etc/lenv_px/lenv_px_sn.etc b/matita/matita/contribs/lambda_delta/basic_2/etc/lenv_px/lenv_px_sn.etc
deleted file mode 100644 (file)
index fddab03..0000000
--- a/matita/matita/contribs/lambda_delta/basic_2/etc/lenv_px/lenv_px_sn.etc
+++ /dev/null
@@ -1,75 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/grammar/lenv_length.ma".
-
-(* SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS **********)
-
-inductive lpx_sn (R:lenv→relation term): relation lenv ≝
-| lpx_sn_stom: lpx_sn R (⋆) (⋆)
-| lpx_sn_pair: ∀I,K1,K2,V1,V2.
-               lpx_sn R K1 K2 → R K1 V1 V2 → lpx_sn R (K1. ⓑ{I} V1) (K2. ⓑ{I} V2)
-.
-
-(* Basic inversion lemmas ***************************************************)
-
-fact lpx_sn_inv_atom1_aux: ∀R,L1,L2. lpx_sn R L1 L2 → L1 = ⋆ → L2 = ⋆.
-#R #L1 #L2 * -L1 -L2
-[ //
-| #I #K1 #K2 #V1 #V2 #_ #_ #H destruct
-]
-qed-.
-
-lemma lpx_sn_inv_atom1: ∀R,L2. lpx_sn R (⋆) L2 → L2 = ⋆.
-/2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
-
-fact lpx_sn_inv_pair1_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K1,V1. L1 = K1. ⓑ{I} V1 →
-                           ∃∃K2,V2. lpx_sn R K1 K2 & R K1 V1 V2 & L2 = K2. ⓑ{I} V2.
-#R #L1 #L2 * -L1 -L2
-[ #J #K1 #V1 #H destruct
-| #I #K1 #K2 #V1 #V2 #HK12 #HV12 #J #L #W #H destruct /2 width=5/
-]
-qed-.
-
-lemma lpx_sn_inv_pair1: ∀R,I,K1,V1,L2. lpx_sn R (K1. ⓑ{I} V1) L2 →
-                        ∃∃K2,V2. lpx_sn R K1 K2 & R K1 V1 V2 & L2 = K2. ⓑ{I} V2.
-/2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
-
-fact lpx_sn_inv_atom2_aux: ∀R,L1,L2. lpx_sn R L1 L2 → L2 = ⋆ → L1 = ⋆.
-#R #L1 #L2 * -L1 -L2
-[ //
-| #I #K1 #K2 #V1 #V2 #_ #_ #H destruct
-]
-qed-.
-
-lemma lpx_sn_inv_atom2: ∀R,L1. lpx_sn R L1 (⋆) → L1 = ⋆.
-/2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
-
-fact lpx_sn_inv_pair2_aux: ∀R,L1,L2. lpx_sn R L1 L2 → ∀I,K2,V2. L2 = K2. ⓑ{I} V2 →
-                           ∃∃K1,V1. lpx_sn R K1 K2 & R K1 V1 V2 & L1 = K1. ⓑ{I} V1.
-#R #L1 #L2 * -L1 -L2
-[ #J #K2 #V2 #H destruct
-| #I #K1 #K2 #V1 #V2 #HK12 #HV12 #J #K #W #H destruct /2 width=5/
-]
-qed-.
-
-lemma lpx_sn_inv_pair2: ∀R,I,L1,K2,V2. lpx_sn R L1 (K2. ⓑ{I} V2) →
-                        ∃∃K1,V1. lpx_sn R K1 K2 & R K1 V1 V2 & L1 = K1. ⓑ{I} V1.
-/2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma lpx_sn_fwd_length: ∀R,L1,L2. lpx_sn R L1 L2 → |L1| = |L2|.
-#R #L1 #L2 #H elim H -L1 -L2 normalize //
-qed-.