X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc%2Fcsup%2Fcsup.etc;h=0a980f6a7fb58bf00b6573563cca64fecea73d08;hb=eb4b3b1b307fc392c36f0be253e6a111553259bc;hp=dcfe086e967e438632075d84f27e83f573b49ddb;hpb=85a33f6b6de49ad8076753643df41f39bbedf802;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/csup/csup.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/csup/csup.etc
index dcfe086e9..0a980f6a7 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/csup/csup.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/csup/csup.etc
@@ -1,94 +1,5 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-notation "hvbox( ⦃ L1, break T1 ⦄ > break ⦃ L2 , break T2 ⦄ )"
-   non associative with precedence 45
-   for @{ 'SupTerm $L1 $T1 $L2 $T2 }.
-
-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 inversion lemmas ***************************************************)
-
-fact csup_inv_atom1_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → ∀J. T1 = ⓪{J} →
-                         ∃∃I,i. ⇩[0, i] L1 ≡ L2.ⓑ{I}T2 & J = LRef i.
-#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2
-[ #I #L #K #V #i #HLK #J #H destruct /2 width=4/
-| #a #I #L #V #T #J #H destruct
-| #a #I #L #V #T #J #H destruct
-| #I #L #V #T #J #H destruct
-| #I #L #V #T #J #H destruct
-]
-qed-.
-
-lemma csup_inv_atom1: ∀J,L1,L2,T2. ⦃L1, ⓪{J}⦄ > ⦃L2, T2⦄ →
-                      ∃∃I,i. ⇩[0, i] L1 ≡ L2.ⓑ{I}T2 & J = LRef i.
-/2 width=3 by csup_inv_atom1_aux/ qed-.
-
-fact csup_inv_bind1_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
-                         ∀b,J,W,U. T1 = ⓑ{b,J}W.U →
-                         (L2 = L1 ∧ T2 = W) ∨
-                         (L2 = L1.ⓑ{J}W ∧ T2 = U).
-#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2
-[ #I #L #K #V #i #_ #b #J #W #U #H destruct
-| #a #I #L #V #T #b #J #W #U #H destruct /3 width=1/
-| #a #I #L #V #T #b #J #W #U #H destruct /3 width=1/
-| #I #L #V #T #b #J #W #U #H destruct
-| #I #L #V #T #b #J #W #U #H destruct
-]
-qed-.
-
-lemma csup_inv_bind1: ∀b,J,L1,L2,W,U,T2. ⦃L1, ⓑ{b,J}W.U⦄ > ⦃L2, T2⦄ →
-                      (L2 = L1 ∧ T2 = W) ∨
-                      (L2 = L1.ⓑ{J}W ∧ T2 = U).
-/2 width=4 by csup_inv_bind1_aux/ qed-.
-
-fact csup_inv_flat1_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
-                         ∀J,W,U. T1 = ⓕ{J}W.U →
-                         L2 = L1 ∧ (T2 = W ∨ T2 = U).
-#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2
-[ #I #L #K #V #i #_ #J #W #U #H destruct
-| #a #I #L #V #T #J #W #U #H destruct
-| #a #I #L #V #T #J #W #U #H destruct
-| #I #L #V #T #J #W #U #H destruct /3 width=1/
-| #I #L #V #T #J #W #U #H destruct /3 width=1/
-]
-qed-.
-
-lemma csup_inv_flat1: ∀J,L1,L2,W,U,T2. ⦃L1, ⓕ{J}W.U⦄ > ⦃L2, T2⦄ →
-                      L2 = L1 ∧ (T2 = W ∨ T2 = U).
-/2 width=4 by csup_inv_flat1_aux/ qed-.
-
 (* 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-.
-
 lemma csup_fwd_ldrop: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
                       ∃i. ⇩[0, i] L1 ≡ L2 ∨ ⇩[0, i] L2 ≡ L1.
 #L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 /3 width=2/ /4 width=2/
@@ -155,3 +66,23 @@ lemma csup_inv_lref2_be: ∀L,U,i. ⦃L, U⦄ > ⦃L, #i⦄ →
 elim (lift_csup_trans_eq … HTU … H) -H -T #T #H
 elim (lift_inv_lref2_be … H ? ?) //
 qed-.
+
+
+fact csup_inv_all4_refl_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → L1 = L2 →
+                             ∨∨ ∃∃a,I,U. T1 = ⓑ{a,I}T2.U
+                              | ∃∃I,W. T1 = ⓕ{I}W.T2
+                              | ∃∃I,U. T1 = ⓕ{I}T2.U.
+#L1 #L2 #T1 #T2 * -L1 -L2 -T1 -T2 /3 width=3/ /3 width=4/
+[ #I #L #K #V #i #HLK #H destruct
+  lapply (ldrop_pair2_fwd_cw … HLK V) -HLK #H
+  elim (lt_refl_false … H)
+| #a #I #L #V #T #H
+  elim (discr_lpair_x_xy … H)
+]
+qed-.
+
+lemma csup_inv_all4_refl: ∀L,T1,T2. ⦃L, T1⦄ > ⦃L, T2⦄ →
+                          ∨∨ ∃∃a,I,U. T1 = ⓑ{a,I}T2.U
+                           | ∃∃I,W. T1 = ⓕ{I}W.T2
+                           | ∃∃I,U. T1 = ⓕ{I}T2.U.
+/2 width=4 by csup_inv_all4_refl_aux/ qed-.