renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
deleted file mode 100644 (file)
index f7375af..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
+++ /dev/null
@@ -1,109 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/notation/relations/ideqsn_3.ma".
-include "basic_2/static/lfxs.ma".
-
-(* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
-
-(* Basic_2A1: was: lleq *)
-definition lfeq: relation3 term lenv lenv ≝
-                 lfxs ceq.
-
-interpretation
-   "syntactic equivalence on referred entries (local environment)"
-   'IdEqSn T L1 L2 = (lfeq T L1 L2).
-
-(* Note: "lfeq_transitive R" is equivalent to "lfxs_transitive ceq R R" *)
-(* Basic_2A1: uses: lleq_transitive *)
-definition lfeq_transitive: predicate (relation3 lenv term term) ≝
-           λR. ∀L2,T1,T2. R L2 T1 T2 → ∀L1. L1 ≡[T1] L2 → R L1 T1 T2.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma lfeq_inv_bind: ∀p,I,L1,L2,V,T. L1 ≡[ⓑ{p,I}V.T] L2 →
-                     ∧∧ L1 ≡[V] L2 & L1.ⓑ{I}V ≡[T] L2.ⓑ{I}V.
-/2 width=2 by lfxs_inv_bind/ qed-.
-
-lemma lfeq_inv_flat: ∀I,L1,L2,V,T. L1 ≡[ⓕ{I}V.T] L2 →
-                     ∧∧ L1 ≡[V] L2 & L1 ≡[T] L2.
-/2 width=2 by lfxs_inv_flat/ qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma lfeq_inv_zero_pair_sn: ∀I,L2,K1,V. K1.ⓑ{I}V ≡[#0] L2 →
-                             ∃∃K2. K1 ≡[V] K2 & L2 = K2.ⓑ{I}V.
-#I #L2 #K1 #V #H
-elim (lfxs_inv_zero_pair_sn … H) -H #K2 #X #HK12 #HX #H destruct
-/2 width=3 by ex2_intro/
-qed-.
-
-lemma lfeq_inv_zero_pair_dx: ∀I,L1,K2,V. L1 ≡[#0] K2.ⓑ{I}V →
-                             ∃∃K1. K1 ≡[V] K2 & L1 = K1.ⓑ{I}V.
-#I #L1 #K2 #V #H
-elim (lfxs_inv_zero_pair_dx … H) -H #K1 #X #HK12 #HX #H destruct
-/2 width=3 by ex2_intro/
-qed-.
-
-lemma lfeq_inv_lref_bind_sn: ∀I1,K1,L2,i. K1.ⓘ{I1} ≡[#↑i] L2 →
-                             ∃∃I2,K2. K1 ≡[#i] K2 & L2 = K2.ⓘ{I2}.
-/2 width=2 by lfxs_inv_lref_bind_sn/ qed-.
-
-lemma lfeq_inv_lref_bind_dx: ∀I2,K2,L1,i. L1 ≡[#↑i] K2.ⓘ{I2} →
-                             ∃∃I1,K1. K1 ≡[#i] K2 & L1 = K1.ⓘ{I1}.
-/2 width=2 by lfxs_inv_lref_bind_dx/ qed-.
-
-(* Basic forward lemmas *****************************************************)
-
-(* Basic_2A1: was: llpx_sn_lrefl *)
-(* Note: this should have been lleq_fwd_llpx_sn *)
-lemma lfeq_fwd_lfxs: ∀R. c_reflexive … R →
-                     ∀L1,L2,T. L1 ≡[T] L2 → L1 ⪤*[R, T] L2.
-#R #HR #L1 #L2 #T * #f #Hf #HL12
-/4 width=7 by lexs_co, cext2_co, ex2_intro/
-qed-.
-
-(* Basic_properties *********************************************************)
-
-lemma frees_lfeq_conf: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≘ f →
-                       ∀L2. L1 ≡[T] L2 → L2 ⊢ 𝐅*⦃T⦄ ≘ f.
-#f #L1 #T #H elim H -f -L1 -T
-[ /2 width=3 by frees_sort/
-| #f #i #Hf #L2 #H2
-  >(lfxs_inv_atom_sn … H2) -L2
-  /2 width=1 by frees_atom/
-| #f #I #L1 #V1 #_ #IH #Y #H2
-  elim (lfeq_inv_zero_pair_sn … H2) -H2 #L2 #HL12 #H destruct
-  /3 width=1 by frees_pair/
-| #f #I #L1 #Hf #Y #H2
-  elim (lfxs_inv_zero_unit_sn … H2) -H2 #g #L2 #_ #_ #H destruct
-  /2 width=1 by frees_unit/
-| #f #I #L1 #i #_ #IH #Y #H2
-  elim (lfeq_inv_lref_bind_sn … H2) -H2 #J #L2 #HL12 #H destruct
-  /3 width=1 by frees_lref/
-| /2 width=1 by frees_gref/
-| #f1V #f1T #f1 #p #I #L1 #V1 #T1 #_ #_ #Hf1 #IHV #IHT #L2 #H2
-  elim (lfeq_inv_bind … H2) -H2 /3 width=5 by frees_bind/
-| #f1V #f1T #f1 #I #L1 #V1 #T1 #_ #_ #Hf1 #IHV #IHT #L2 #H2
-  elim (lfeq_inv_flat … H2) -H2 /3 width=5 by frees_flat/
-]
-qed-.
-
-(* Basic_2A1: removed theorems 10:
-              lleq_ind lleq_fwd_lref
-              lleq_fwd_drop_sn lleq_fwd_drop_dx
-              lleq_skip lleq_lref lleq_free
-              lleq_Y lleq_ge_up lleq_ge
-               
-*)