- we set up the support for the "bt-reduction" of Automath literature

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / substitution / csup.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/substitution/csup.ma b/matita/matita/contribs/lambda_delta/basic_2/substitution/csup.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambda_delta/basic_2/substitution/csup.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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.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-.