X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpxs_lfdeq.ma;h=2a331abf9b0c73ca2fc8f46b0650d38002ed3120;hb=6167cca50de37eba76a062537b24f7caef5b34f2;hp=73119ad5363c6e833864af2620baaaf003682826;hpb=6d49221c1fefe6a2c5bddb3db24d3698414a700f;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma
index 73119ad53..2a331abf9 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma
@@ -21,8 +21,8 @@ include "basic_2/rt_computation/cpxs_tdeq.ma".
 
 (* Basic_2A1: was just: lleq_cpxs_trans *) 
 lemma lfdeq_cpxs_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
-                        ∀L2. L2 ≡[h, o, T0] L0 →
-                        ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≡[h, o] T1.
+                        ∀L2. L2 ≛[h, o, T0] L0 →
+                        ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≛[h, o] T1.
 #h #o #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
 #T0 #T #HT0 #_ #IH #L2 #HL2
 elim (lfdeq_cpx_trans … HL2 … HT0) #U1 #H1 #H2
@@ -33,17 +33,17 @@ qed-.
 
 (* Basic_2A1: was just: cpxs_lleq_conf *) 
 lemma cpxs_lfdeq_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
-                        ∀L2. L0 ≡[h, o, T0] L2 →
-                        ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≡[h, o] T1.
+                        ∀L2. L0 ≛[h, o, T0] L2 →
+                        ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≛[h, o] T1.
 /3 width=3 by lfdeq_cpxs_trans, lfdeq_sym/ qed-.
 
 (* Basic_2A1: was just: cpxs_lleq_conf_dx *) 
 lemma cpxs_lfdeq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h] T2 →
-                          ∀L1. L1 ≡[h, o, T1] L2 → L1 ≡[h, o, T2] L2.
+                          ∀L1. L1 ≛[h, o, T1] L2 → L1 ≛[h, o, T2] L2.
 #h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lfdeq_conf_dx/
 qed-.
 
 (* Basic_2A1: was just: lleq_conf_sn *) 
 lemma cpxs_lfdeq_conf_sn: ∀h,o,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈*[h] T2 →
-                          ∀L2. L1 ≡[h, o, T1] L2 → L1 ≡[h, o, T2] L2.
+                          ∀L2. L1 ≛[h, o, T1] L2 → L1 ≛[h, o, T2] L2.
 /4 width=6 by cpxs_lfdeq_conf_dx, lfdeq_sym/ qed-.