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-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
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-(**************************************************************************)
-
-include "basic_2/substitution/ldrop.ma".
-
-(* SUPCLOSURE ***************************************************************)
-
-inductive csup: bi_relation lenv term ≝
-| csup_lref : ∀I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → csup L (#i) K V
-| csup_bind_sn: ∀a,I,L,V,T. csup L (ⓑ{a,I}V.T) L V
-| csup_bind_dx: ∀a,I,L,V,T. csup L (ⓑ{a,I}V.T) (L.ⓑ{I}V) T
-| csup_flat_sn: ∀I,L,V,T. csup L (ⓕ{I}V.T) L V
-| csup_flat_dx: ∀I,L,V,T. csup L (ⓕ{I}V.T) L T
-.
-
-interpretation
- "structural predecessor (closure)"
- 'SupTerm L1 T1 L2 T2 = (csup L1 T1 L2 T2).
-
-(* Basic forward lemmas *****************************************************)
-
-lemma csup_fwd_cw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → #{L2, T2} < #{L1, T1}.
-#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 /width=1/ /2 width=4 by ldrop_pair2_fwd_cw/
-qed-.