- former llpx_sn an lleq reactivated as lfxs and lfeq

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfeq_lfeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq_lfeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq_lfeq.ma
new file mode 100644 (file)
index 0000000..a6f5647
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq_lfeq.ma
@@ -0,0 +1,56 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/lreq_lreq.ma".
+include "basic_2/static/frees_frees.ma".
+include "basic_2/static/lfxs_lfxs.ma".
+include "basic_2/static/lfeq_lreq.ma".
+
+(* EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *******************)
+
+(* Main properties **********************************************************)
+
+theorem lfeq_bind: ∀I,L1,L2,V1,V2,T,p.
+                   L1 ≡[V1] L2 → L1.ⓑ{I}V1 ≡[T] L2.ⓑ{I}V2 →
+                   L1 ≡[ⓑ{p,I}V1.T] L2.
+/2 width=2 by lfxs_bind/ qed.
+
+theorem lfeq_flat: ∀I,L1,L2,V,T. L1 ≡[V] L2 → L1 ≡[T] L2 →
+                   L1 ≡[ⓕ{I}V.T] L2.
+/2 width=1 by lfxs_flat/ qed.
+
+(* Note: /2 width=3 by lfeq_lfxs_trans/ *)
+theorem lfeq_trans: ∀T. Transitive … (lfeq T).
+#T #L1 #L * #f1 #Hf1 #HL1 #L2 * #f2 #Hf2 #HL2
+lapply (frees_lreq_conf … Hf1 … HL1) #H0
+lapply (frees_mono … Hf2 … H0) -Hf2 -H0
+/4 width=7 by lreq_trans, lexs_eq_repl_back, ex2_intro/
+qed-.
+
+theorem lfeq_canc_sn: ∀T. left_cancellable … (lfeq T).
+/3 width=3 by lfeq_trans, lfeq_sym/ qed-.
+
+theorem lfeq_canc_dx: ∀T. right_cancellable … (lfeq T).
+/3 width=3 by lfeq_trans, lfeq_sym/ qed-.
+
+(* Advanced properies on negated lazy equivalence *****************************)
+
+(* Note: for use in auto, works with /4 width=8/ so lfeq_canc_sn is preferred *) 
+lemma lfeq_nlfeq_trans: ∀T,L1,L. L1 ≡[T] L →
+                        ∀L2. (L ≡[T] L2 → ⊥) → (L1 ≡[T] L2 → ⊥).
+/3 width=3 by lfeq_canc_sn/ qed-.
+
+lemma nlfeq_lfeq_div: ∀T,L2,L. L2 ≡[T] L →
+                      ∀L1. (L1 ≡[T] L → ⊥) → (L1 ≡[T] L2 → ⊥).
+/3 width=3 by lfeq_trans/ qed-.