matita/matita/contribs/lambda_delta/basic_2/substitution/csup.ma

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  14
  15 include "basic_2/substitution/ldrop.ma".
  16
  17 (* SUPCLOSURE ***************************************************************)
  18
  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
  25 .
  26
  27 interpretation
  28    "structural predecessor (closure)"
  29    'SupTerm L1 T1 L2 T2 = (csup L1 T1 L2 T2).
  30
  31 (* Basic forward lemmas *****************************************************)
  32
  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/
  35 qed-.