-(* Advanced inversion lemmas ************************************************)
+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
-lemma sta_inv_refl_pos: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h] T → ⊥.
-#h #g #G #L #T #l #H1T #HTT
-lapply (sta_da_conf … HTT … H1T) -HTT <minus_plus_m_m #H2T
-lapply (da_mono … H2T … H1T) -h -G -L -T #H
-elim (plus_xySz_x_false 0 l 0 ?) //
+include "basic_2/static/da_lift.ma".
+
+(* DEGREE ASSIGNMENT FOR TERMS **********************************************)
+
+(* Main properties **********************************************************)
+
+theorem da_mono: ∀h,o,G,L,T,d1. ⦃G, L⦄ ⊢ T ▪[h, o] d1 →
+ ∀d2. ⦃G, L⦄ ⊢ T ▪[h, o] d2 → d1 = d2.
+#h #o #G #L #T #d1 #H elim H -G -L -T -d1
+[ #G #L #s #d1 #Hkd1 #d2 #H
+ lapply (da_inv_sort … H) -G -L #Hkd2
+ >(deg_mono … Hkd2 … Hkd1) -h -s -d2 //
+| #G #L #K #V #i #d1 #HLK #_ #IHV #d2 #H
+ elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0 #HV0 [| #Hd0 ]
+ lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct /2 width=1 by/
+| #G #L #K #W #i #d1 #HLK #_ #IHW #d2 #H
+ elim (da_inv_lref … H) -H * #K0 #W0 [| #d0 ] #HLK0 #HW0 [| #Hd0 ]
+ lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct /3 width=1 by eq_f/
+| #a #I #G #L #V #T #d1 #_ #IHT #d2 #H
+ lapply (da_inv_bind … H) -H /2 width=1 by/
+| #I #G #L #V #T #d1 #_ #IHT #d2 #H
+ lapply (da_inv_flat … H) -H /2 width=1 by/
+]
qed-.