more additions and corrections for the article

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / etc / scl / scl_scl.etc

diff --git a/matita/matita/contribs/lambdadelta/static_2/etc/scl/scl_scl.etc b/matita/matita/contribs/lambdadelta/static_2/etc/scl/scl_scl.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/static_2/etc/scl/scl_scl.etc
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/relocation/scl.ma".
+
+(* CLEAR FOR LOCAL ENVIRONMENTS ON SELECTED ENTRIES *************************)
+
+(* Main properties **********************************************************)
+
+theorem scl_fix: ∀f,L1,L. L1 ⊐ⓧ[f] L →
+                 ∀L2. L ⊐ⓧ[f] L2 → L = L2.
+#f #L1 #L #H @(scl_ind … H) -f -L1 -L
+[ #f #L2 #H
+  >(scl_inv_atom_sn … H) -L2 //
+| #f #I #K1 #K2 #_ #IH #L2 #H
+  elim (scl_inv_push_sn … H) -H /3 width=1 by eq_f2/
+| #f #I #K1 #K2 #_ #IH #L2 #H
+  elim (scl_inv_next_sn … H) -H /3 width=1 by eq_f2/
+]
+qed-.
+
+theorem scl_trans: ∀f. Transitive … (scl f).
+#f #L1 #L #H1 #L2 #H2
+<(scl_fix … H1 … H2) -L2 //
+qed-.