- lambda_delta: programmed renaming to lambdadelta

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / etc / csup / csups.etc

diff --git a/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csups.etc b/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csups.etc
deleted file mode 100644 (file)
index 7f58794..0000000
--- a/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csups.etc
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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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-notation "hvbox( ⦃ L1, break T1 ⦄ > * break ⦃ L2 , break T2 ⦄ )"
-   non associative with precedence 45
-   for @{ 'SupTermStar $L1 $T1 $L2 $T2 }.
-
-include "basic_2/substitution/csup.ma".
-include "basic_2/unfold/csupp.ma".
-
-(* STAR-ITERATED SUPCLOSURE *************************************************)
-
-definition csups: bi_relation lenv term ≝ bi_star … csup.
-
-interpretation "star-iterated structural predecessor (closure)"
-   'SupTermStar L1 T1 L2 T2 = (csups L1 T1 L2 T2).
-
-(* Basic eliminators ********************************************************)
-
-lemma csups_ind: ∀L1,T1. ∀R:relation2 lenv term. R L1 T1 →
-                 (∀L,L2,T,T2. ⦃L1, T1⦄ >* ⦃L, T⦄ → ⦃L, T⦄ > ⦃L2, T2⦄ → R L T → R L2 T2) →
-                 ∀L2,T2. ⦃L1, T1⦄ >* ⦃L2, T2⦄ → R L2 T2.
-#L1 #T1 #R #IH1 #IH2 #L2 #T2 #H
-@(bi_star_ind … IH1 IH2 ? ? H)
-qed-.
-
-lemma csups_ind_dx: ∀L2,T2. ∀R:relation2 lenv term. R L2 T2 →
-                    (∀L1,L,T1,T. ⦃L1, T1⦄ > ⦃L, T⦄ → ⦃L, T⦄ >* ⦃L2, T2⦄ → R L T → R L1 T1) →
-                    ∀L1,T1. ⦃L1, T1⦄ >* ⦃L2, T2⦄ → R L1 T1.
-#L2 #T2 #R #IH1 #IH2 #L1 #T1 #H
-@(bi_star_ind_dx … IH1 IH2 ? ? H)
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma csups_refl: bi_reflexive … csups.
-/2 width=1/ qed.
-
-lemma csupp_csups: ∀L1,L2,T1,T2. ⦃L1, T1⦄ >+ ⦃L2, T2⦄ → ⦃L1, T1⦄ >* ⦃L2, T2⦄.
-/2 width=1/ qed.
-
-lemma csup_csups: ∀L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → ⦃L1, T1⦄ >* ⦃L2, T2⦄.
-/2 width=1/ qed.
-
-lemma csups_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ >* ⦃L, T⦄ → ⦃L, T⦄ > ⦃L2, T2⦄ →
-                    ⦃L1, T1⦄ >* ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma csups_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ > ⦃L, T⦄ → ⦃L, T⦄ >* ⦃L2, T2⦄ →
-                    ⦃L1, T1⦄ >* ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma csups_csupp_csupp: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ >* ⦃L, T⦄ →
-                         ⦃L, T⦄ >+ ⦃L2, T2⦄ → ⦃L1, T1⦄ >+ ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma csupp_csups_csupp: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ >+ ⦃L, T⦄ →
-                          ⦃L, T⦄ >* ⦃L2, T2⦄ → ⦃L1, T1⦄ >+ ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma csups_fwd_cw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ >* ⦃L2, T2⦄ → #{L2, T2} ≤ #{L1, T1}.
-#L1 #L2 #T1 #T2 #H @(csups_ind … H) -L2 -T2 //
-/4 width=3 by csup_fwd_cw, lt_to_le_to_lt, lt_to_le/ (**) (* slow even with trace *)
-qed-.
-
-(* Advanced inversion lemmas for csupp **************************************)
-
-lemma csupp_inv_atom1_csups: ∀J,L1,L2,T2. ⦃L1, ⓪{J}⦄ >+ ⦃L2, T2⦄ →
-                             ∃∃I,K,V,i. ⇩[0, i] L1 ≡ K.ⓑ{I}V &
-                             ⦃K, V⦄ >* ⦃L2, T2⦄ & J = LRef i.
-#J #L1 #L2 #T2 #H @(csupp_ind … H) -L2 -T2
-[ #L2 #T2 #H
-  elim (csup_inv_atom1 … H) -H * #i #HL12 #H destruct /2 width=7/
-| #L #T #L2 #T2 #_ #HT2 * #I #K #V #i #HLK #HVT #H destruct /3 width=8/
-]
-qed-.
-
-lemma csupp_inv_bind1_csups: ∀b,J,L1,L2,W,U,T2. ⦃L1, ⓑ{b,J}W.U⦄ >+ ⦃L2, T2⦄ →
-                             ⦃L1, W⦄ >* ⦃L2, T2⦄ ∨ ⦃L1.ⓑ{J}W, U⦄ >* ⦃L2, T2⦄.
-#b #J #L1 #L2 #W #U #T2 #H @(csupp_ind … H) -L2 -T2
-[ #L2 #T2 #H
-  elim (csup_inv_bind1 … H) -H * #H1 #H2 destruct /2 width=1/
-| #L #T #L2 #T2 #_ #HT2 * /3 width=4/
-]
-qed-.
-
-lemma csupp_inv_flat1_csups: ∀J,L1,L2,W,U,T2. ⦃L1, ⓕ{J}W.U⦄ >+ ⦃L2, T2⦄ →
-                             ⦃L1, W⦄ >* ⦃L2, T2⦄ ∨ ⦃L1, U⦄ >* ⦃L2, T2⦄.
-#J #L1 #L2 #W #U #T2 #H @(csupp_ind … H) -L2 -T2
-[ #L2 #T2 #H
-  elim (csup_inv_flat1 … H) -H #H1 * #H2 destruct /2 width=1/
-| #L #T #L2 #T2 #_ #HT2 * /3 width=4/
-]
-qed-.