X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs_fsle.ma;h=514e63defcfbacafef16a6dff3f4726e0065a879;hb=5c186c72f508da0849058afeecc6877cd9ed6303;hp=011748dbfd44b20e4c68115c2a9645b2151ce0ca;hpb=f7296f9cf2ee73465a374942c46b138f35c42ccb;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fsle.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fsle.ma
index 011748dbf..514e63def 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fsle.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fsle.ma
@@ -31,9 +31,9 @@ definition lfxs_fsle_compatible: predicate (relation3 …) ≝ λRN.
 (* Basic inversions with free variables inclusion for restricted closures ***)
 
 lemma frees_lexs_conf: ∀R. lfxs_fsge_compatible R →
-                       ∀L1,T,f1. L1 ⊢ 𝐅*⦃T⦄ ≡ f1 →
+                       ∀L1,T,f1. L1 ⊢ 𝐅*⦃T⦄ ≘ f1 →
                        ∀L2. L1 ⪤*[cext2 R, cfull, f1] L2 →
-                       ∃∃f2. L2 ⊢ 𝐅*⦃T⦄ ≡ f2 & f2 ⊆ f1.
+                       ∃∃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
 @(fsle_frees_trans_eq … H2L … Hf1) /3 width=4 by lexs_fwd_length, sym_eq/
@@ -165,7 +165,7 @@ elim (lexs_conf … HL01 … HL02) /2 width=3 by ex2_intro/ [ | -HL01 -HL02 ]
 qed-.
 
 theorem lfxs_trans_fsle: ∀R1,R2,R3.
-                         lfxs_fsle_compatible R1 → lfxs_transitive_next R1 R2 R3 →
+                         lfxs_fsle_compatible R1 → f_transitive_next R1 R2 R3 →
                          ∀L1,L,T. L1 ⪤*[R1, T] L →
                          ∀L2. L ⪤*[R2, T] L2 → L1 ⪤*[R3, T] L2.
 #R1 #R2 #R3 #H1R #H2R #L1 #L #T #H