--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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-.