update in ground_2 and basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
index f827a1f20a9f566ab4e2630b0fb5508e11662c30..cdf65c7c0e71cc2ea04c8b1da0bb9bb2aad5f628 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
@@ -15,8 +15,8 @@
 include "basic_2/relocation/lexs_length.ma".
 include "basic_2/relocation/lexs_lexs.ma".
 include "basic_2/static/frees_drops.ma".
-include "basic_2/static/fle_fle.ma".
-include "basic_2/static/lfxs.ma".
+include "basic_2/static/fsle_fsle.ma".
+include "basic_2/static/lfxs_fsle.ma".
 
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
 
@@ -27,13 +27,13 @@ lemma lfxs_inv_frees: ∀R,L1,L2,T. L1 ⪤*[R, T] L2 →
 #R #L1 #L2 #T * /3 width=6 by frees_mono, lexs_eq_repl_back/
 qed-.
 
-lemma frees_lexs_conf: ∀R. lfxs_fle_compatible R →
+lemma frees_lexs_conf: ∀R. lfxs_fsle_compatible R →
                        ∀L1,T,f1. L1 ⊢ 𝐅*⦃T⦄ ≡ f1 →
                        ∀L2. L1 ⪤*[cext2 R, cfull, f1] L2 →
                        ∃∃f2. L2 ⊢ 𝐅*⦃T⦄ ≡ f2 & f2 ⊆ f1.
 #R #HR #L1 #T #f1 #Hf1 #L2 #H1L
 lapply (HR L1 L2 T ?) /2 width=3 by ex2_intro/ #H2L
-@(fle_frees_trans_eq … H2L … Hf1) /3 width=4 by lexs_fwd_length, sym_eq/
+@(fsle_frees_trans_eq … H2L … Hf1) /3 width=4 by lexs_fwd_length, sym_eq/
 qed-.
 
 (* Properties with free variables inclusion for restricted closures *********)
@@ -48,7 +48,7 @@ qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma lfxs_sym: ∀R. lfxs_fle_compatible R →
+lemma lfxs_sym: ∀R. lfxs_fsle_compatible R →
                 (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
                 ∀T. symmetric … (lfxs R T).
 #R #H1R #H2R #T #L1 #L2
@@ -67,7 +67,7 @@ elim (lexs_dec (cext2 R) cfull … L1 L2 f)
 qed-.
 
 lemma lfxs_pair_sn_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
-                          lfxs_fle_compatible R1 →
+                          lfxs_fsle_compatible R1 →
                           ∀L1,L2,V. L1 ⪤*[R1, V] L2 → ∀I,T.
                           ∃∃L. L1 ⪤*[R1, ②{I}V.T] L & L ⪤*[R2, V] L2.
 #R1 #R2 #HR1 #HR2 #HR #L1 #L2 #V * #f #Hf #HL12 * [ #p ] #I #T
@@ -86,7 +86,7 @@ elim (frees_lexs_conf … Hf … H) -Hf -H
 qed-.
 
 lemma lfxs_flat_dx_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
-                          lfxs_fle_compatible R1 →
+                          lfxs_fsle_compatible R1 →
                           ∀L1,L2,T. L1 ⪤*[R1, T] L2 → ∀I,V.
                           ∃∃L. L1 ⪤*[R1, ⓕ{I}V.T] L & L ⪤*[R2, T] L2.
 #R1 #R2 #HR1 #HR2 #HR #L1 #L2 #T * #f #Hf #HL12 #I #V
@@ -102,7 +102,7 @@ elim (frees_lexs_conf … Hf … H) -Hf -H
 qed-.
 
 lemma lfxs_bind_dx_split: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
-                          lfxs_fle_compatible R1 →
+                          lfxs_fsle_compatible R1 →
                           ∀I,L1,L2,V1,T. L1.ⓑ{I}V1 ⪤*[R1, T] L2 → ∀p.
                           ∃∃L,V. L1 ⪤*[R1, ⓑ{p,I}V1.T] L & L.ⓑ{I}V ⪤*[R2, T] L2 & R1 L1 V1 V.
 #R1 #R2 #HR1 #HR2 #HR #I #L1 #L2 #V1 #T * #f #Hf #HL12 #p
@@ -122,7 +122,7 @@ elim (frees_lexs_conf … Hf … H0) -Hf -H0
 qed-.
 
 lemma lfxs_bind_dx_split_void: ∀R1,R2. (∀L. reflexive … (R1 L)) → (∀L. reflexive … (R2 L)) →
-                               lfxs_fle_compatible R1 →
+                               lfxs_fsle_compatible R1 →
                                ∀L1,L2,T. L1.ⓧ ⪤*[R1, T] L2 → ∀p,I,V.
                                ∃∃L. L1 ⪤*[R1, ⓑ{p,I}V.T] L & L.ⓧ ⪤*[R2, T] L2.
 #R1 #R2 #HR1 #HR2 #HR #L1 #L2 #T * #f #Hf #HL12 #p #I #V
@@ -169,8 +169,8 @@ lapply (lexs_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫱f2))
 qed.
 
 theorem lfxs_conf: ∀R1,R2.
-                   lfxs_fle_compatible R1 →
-                   lfxs_fle_compatible R2 →
+                   lfxs_fsle_compatible R1 →
+                   lfxs_fsle_compatible R2 →
                    R_confluent2_lfxs R1 R2 R1 R2 →
                    ∀T. confluent2 … (lfxs R1 T) (lfxs R2 T).
 #R1 #R2 #HR1 #HR2 #HR12 #T #L0 #L1 * #f1 #Hf1 #HL01 #L2 * #f #Hf #HL02