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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 "basic_2/substitution/ldrop_ldrop.ma".
-include "basic_2/static/ssta.ma".
-
-(* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
-
-(* Main properties **********************************************************)
-
-(* Note: apparently this was missing in basic_1 *)
-theorem ssta_mono: ∀h,g,L,T,U1,l1. ⦃h, L⦄ ⊢ T •[g, l1] U1 →
- ∀U2,l2. ⦃h, L⦄ ⊢ T •[g, l2] U2 → l1 = l2 ∧ U1 = U2.
-#h #g #L #T #U1 #l1 #H elim H -L -T -U1 -l1
-[ #L #k #l #Hkl #X #l2 #H
- elim (ssta_inv_sort1 … H) -H #Hkl2 #H destruct
- >(deg_mono … Hkl2 … Hkl) -g -L -l2 /2 width=1/
-| #L #K #V #W #U1 #i #l1 #HLK #_ #HWU1 #IHVW #U2 #l2 #H
- elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 [2: #l0] #HLK0 #HVW0 #HW0U2
- lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
- lapply (IHVW … HVW0) -IHVW -HVW0 * #H1 #H2 destruct
- >(lift_mono … HWU1 … HW0U2) -W0 -U1 /2 width=1/
-| #L #K #W #V #U1 #i #l1 #HLK #_ #HWU1 #IHWV #U2 #l2 #H
- elim (ssta_inv_lref1 … H) -H * #K0 #W0 #V0 [2: #l0 ] #HLK0 #HWV0 #HV0U2
- lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
- lapply (IHWV … HWV0) -IHWV -HWV0 * #H1 #H2 destruct
- >(lift_mono … HWU1 … HV0U2) -W -U1 /2 width=1/
-| #a #I #L #V #T #U1 #l1 #_ #IHTU1 #X #l2 #H
- elim (ssta_inv_bind1 … H) -H #U2 #HTU2 #H destruct
- elim (IHTU1 … HTU2) -T /3 width=1/
-| #L #V #T #U1 #l1 #_ #IHTU1 #X #l2 #H
- elim (ssta_inv_appl1 … H) -H #U2 #HTU2 #H destruct
- elim (IHTU1 … HTU2) -T /3 width=1/
-| #L #W1 #T #U1 #l1 #_ #IHTU1 #U2 #l2 #H
- lapply (ssta_inv_cast1 … H) -H #HTU2
- elim (IHTU1 … HTU2) -T /2 width=1/
-]
-qed-.