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15 include "basic_2/substitution/ldrop.ma".
17 (* SUPCLOSURE ***************************************************************)
19 inductive csup: bi_relation lenv term ≝
20 | csup_lref : ∀I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → csup L (#i) K V
21 | csup_bind_sn: ∀a,I,L,V,T. csup L (ⓑ{a,I}V.T) L V
22 | csup_bind_dx: ∀a,I,L,V,T. csup L (ⓑ{a,I}V.T) (L.ⓑ{I}V) T
23 | csup_flat_sn: ∀I,L,V,T. csup L (ⓕ{I}V.T) L V
24 | csup_flat_dx: ∀I,L,V,T. csup L (ⓕ{I}V.T) L T
28 "structural predecessor (closure)"
29 'SupTerm L1 T1 L2 T2 = (csup L1 T1 L2 T2).
31 (* Basic forward lemmas *****************************************************)
33 lemma csup_fwd_cw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → #{L2, T2} < #{L1, T1}.
34 #L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 /width=1/ /2 width=4 by ldrop_pair2_fwd_cw/