renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / seq_seq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/seq_seq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/seq_seq.ma
new file mode 100644 (file)
index 0000000..cd8dbe3
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/seq_seq.ma
@@ -0,0 +1,37 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/syntax/ceq_ext_ceq_ext.ma".
+include "basic_2/relocation/sex_sex.ma".
+
+(* SYNTACTIC EQUIVALENCE FOR SELECTED LOCAL ENVIRONMENTS ********************)
+
+(* Main properties **********************************************************)
+
+theorem seq_trans: ∀f. Transitive … (seq f).
+/3 width=5 by sex_trans, ceq_ext_trans/ qed-.
+
+theorem seq_canc_sn: ∀f. left_cancellable … (seq f).
+/3 width=3 by sex_canc_sn, seq_trans, seq_sym/ qed-.
+
+theorem seq_canc_dx: ∀f. right_cancellable … (seq f).
+/3 width=3 by sex_canc_dx, seq_trans, seq_sym/ qed-.
+
+theorem seq_join: ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
+                  ∀f. f1 ⋓ f2 ≘ f → L1 ≡[f] L2.
+/2 width=5 by sex_join/ qed-.
+
+theorem seq_meet: ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
+                  ∀f. f1 ⋒ f2 ≘ f → L1 ≡[f] L2.
+/2 width=5 by sex_meet/ qed-.