- advances on lfxs for lfpxs

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / lfxs / lfxs_lfxs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/lfxs/lfxs_lfxs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/lfxs/lfxs_lfxs.etc
index 307740bea9bec99c01eea85bd9d5fc66208d4d55..4ca71664c672f7e9dd713effa3ab2f586af3b872 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/lfxs/lfxs_lfxs.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/lfxs/lfxs_lfxs.etc
@@ -1,41 +1,3 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/relocation/lexs_lexs.ma".
-include "basic_2/static/frees_fqup.ma".
-include "basic_2/static/frees_frees.ma".
-include "basic_2/static/lfxs.ma".
-
-(* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
-
-(* Main properties **********************************************************)
-
-theorem lfxs_bind: ∀R,p,I,L1,L2,V1,V2,T.
-                   L1 ⦻*[R, V1] L2 → L1.ⓑ{I}V1 ⦻*[R, T] L2.ⓑ{I}V2 →
-                   L1 ⦻*[R, ⓑ{p,I}V1.T] L2.
-#R #p #I #L1 #L2 #V1 #V2 #T * #f1 #HV #Hf1 * #f2 #HT #Hf2
-elim (lexs_fwd_pair … Hf2) -Hf2 #Hf2 #_ elim (sor_isfin_ex f1 (⫱f2))
-/3 width=7 by frees_fwd_isfin, frees_bind, lexs_join, isfin_tl, ex2_intro/
-qed.
-
-theorem lfxs_flat: ∀R,I,L1,L2,V,T.
-                   L1 ⦻*[R, V] L2 → L1 ⦻*[R, T] L2 →
-                   L1 ⦻*[R, ⓕ{I}V.T] L2.
-#R #I #L1 #L2 #V #T * #f1 #HV #Hf1 * #f2 #HT #Hf2 elim (sor_isfin_ex f1 f2)
-/3 width=7 by frees_fwd_isfin, frees_flat, lexs_join, ex2_intro/
-qed.
-
 theorem lfxs_trans: ∀R. lexs_frees_confluent R cfull →
                     ∀T. Transitive … (lfxs R T).
 #R #H1R #T #L1 #L * #f1 #Hf1 #HL1 #L2 * #f2 #Hf2 #HL2
@@ -47,24 +9,3 @@ lapply (sle_lexs_trans … HL1 … H1) -HL1 // #Hl1
 
 /4 width=7 by lreq_trans, lexs_eq_repl_back, ex2_intro/
 qed-.
-
-theorem lfxs_conf: ∀R. lexs_frees_confluent R cfull →
-                   R_confluent2_lfxs R R R R →
-                   ∀T. confluent … (lfxs R T).
-#R #H1R #H2R #T #L0 #L1 * #f1 #Hf1 #HL01 #L2 * #f #Hf #HL02
-lapply (frees_mono … Hf1 … Hf) -Hf1 #Hf12
-lapply (lexs_eq_repl_back … HL01 … Hf12) -f1 #HL01
-elim (lexs_conf … HL01 … HL02) /2 width=3 by ex2_intro/ [ | -HL01 -HL02 ]
-[ #L #HL1 #HL2
-  elim (H1R … Hf … HL01) -HL01 #f1 #Hf1 #H1
-  elim (H1R … Hf … HL02) -HL02 #f2 #Hf2 #H2
-  lapply (sle_lexs_trans … HL1 … H1) // -HL1 -H1 #HL1
-  lapply (sle_lexs_trans … HL2 … H2) // -HL2 -H2 #HL2
-  /3 width=5 by ex2_intro/
-| #g #I #K0 #V0 #n #HLK0 #Hgf #V1 #HV01 #V2 #HV02 #K1 #HK01 #K2 #HK02
-  elim (frees_drops_next … Hf … HLK0 … Hgf) -Hf -HLK0 -Hgf #g0 #Hg0 #H0
-  lapply (sle_lexs_trans … HK01 … H0) // -HK01 #HK01
-  lapply (sle_lexs_trans … HK02 … H0) // -HK02 #HK02
-  elim (H2R … HV01 … HV02 K1 … K2) /2 width=3 by ex2_intro/
-]
-qed-.