-(**************************************************************************)
-(* ___ *)
-(* ||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/substitution/csup.ma".
-
-(* SUPCLOSURE ***************************************************************)
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma csup_inv_ldrop: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
- ∀J,W,j. ⇩[0, j] L1 ≡ L2.ⓑ{J}W → T1 = #j ∧ T2 = W.
-#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2
-[ #I #L #K #V #i #HLKV #J #W #j #HLKW
- elim (ldrop_conf_div … HLKV … HLKW) -L /2 width=1/
-| #a
-| #a
-]
-#I #L #V #T #J #W #j #H
-lapply (ldrop_pair2_fwd_cw … H W) -H #H
-[2: lapply (transitive_lt (#{L,W}) … H) /2 width=1/ -H #H ]
-elim (lt_refl_false … H)
-qed-.
-
-(* Main forward lemmas ******************************************************)
-
-theorem csup_trans_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ > ⦃L0, T2⦄ →
- ∀T3. ⦃L0, T2⦄ > ⦃L, T3⦄ →
- L = L0 ∨ ⦃L, T1⦄ > ⦃L, T3⦄.
-#L #L0 #T1 #T2 * -L -L0 -T1 -T2 /2 width=1/
-[ #I #L0 #K0 #V0 #i #HLK0 #T3 #H
- lapply (ldrop_pair2_fwd_cw … HLK0 T3) -HLK0 #H1
- lapply (csup_fwd_cw … H) -H #H2
- lapply (transitive_lt … H1 H2) -H1 -H2 #H
- elim (lt_refl_false … H)
-| #a #I #L0 #V2 #T2 #T3 #HT23
- elim (csup_inv_ldrop … HT23 I V2 0 ?) -HT23 // #H1 #H2 destruct /2 width=1/
- qed-.