--- /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 "basic_2/substitution/drop_drop.ma".
+include "basic_2/static/sta.ma".
+
+(* STATIC TYPE ASSIGNMENT ON TERMS ******************************************)
+
+(* Main properties **********************************************************)
+
+(* Note: apparently this was missing in basic_1 *)
+theorem sta_mono: ∀h,G,L. singlevalued … (sta h G L).
+#h #G #L #T #U1 #H elim H -G -L -T -U1
+[ #G #L #k #X #H >(sta_inv_sort1 … H) -X //
+| #G #L #K #V #W #U1 #i #HLK #_ #HWU1 #IHVW #U2 #H
+ elim (sta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HW0U2
+ lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
+ lapply (IHVW … HVW0) -IHVW -HVW0 #H destruct
+ >(lift_mono … HWU1 … HW0U2) -W0 -U1 //
+| #G #L #K #W #V #U1 #i #HLK #_ #HWU1 #IHWV #U2 #H
+ elim (sta_inv_lref1 … H) -H * #K0 #W0 #V0 #HLK0 #HWV0 #HV0U2
+ lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
+ lapply (IHWV … HWV0) -IHWV -HWV0 #H destruct
+ >(lift_mono … HWU1 … HV0U2) -W -U1 //
+| #a #I #G #L #V #T #U1 #_ #IHTU1 #X #H
+ elim (sta_inv_bind1 … H) -H #U2 #HTU2 #H destruct /3 width=1 by eq_f/
+| #G #L #V #T #U1 #_ #IHTU1 #X #H
+ elim (sta_inv_appl1 … H) -H #U2 #HTU2 #H destruct /3 width=1 by eq_f/
+| #G #L #W #T #U1 #_ #IHTU1 #U2 #H
+ lapply (sta_inv_cast1 … H) -H /2 width=1 by/
+]
+qed-.