update in staic_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / i_static / rexs_lex.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_lex.ma b/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_lex.ma
index a5a1a42dc3b0cc15ae9025b7ba4255dedabfa333..9d582d83b4dc81b1af65bd643832e438c7b63146 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_lex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_lex.ma
@@ -21,13 +21,15 @@ include "static_2/i_static/rexs_fqup.ma".
 
 (* Properties with generic extension of a context sensitive relation ********)
 
-lemma rexs_lex (R): c_reflexive … R →
+lemma rexs_lex (R):
+      c_reflexive … R →
       ∀L1,L2,T. L1 ⪤[CTC … R] L2 → L1 ⪤*[R,T] L2.
 #R #HR #L1 #L2 #T *
 /5 width=7 by rexs_tc, sex_inv_tc_dx, sex_co, ext2_inv_tc, ext2_refl/
 qed.
 
-lemma rexs_lex_req (R): c_reflexive … R →
+lemma rexs_lex_req (R):
+      c_reflexive … R →
       ∀L1,L. L1 ⪤[CTC … R] L → ∀L2,T. L ≡[T] L2 → L1 ⪤*[R,T] L2.
 /3 width=3 by rexs_lex, rexs_step_dx, req_fwd_rex/ qed.
 
@@ -36,7 +38,7 @@ lemma rexs_lex_req (R): c_reflexive … R →
 (* Note: s_rs_transitive_lex_inv_isid could be invoked in the last auto but makes it too slow *)
 lemma rexs_inv_lex_req (R):
       c_reflexive … R → rex_fsge_compatible R →
-      s_rs_transitive … R (λ_.lex R) → req_transitive R →
+      s_rs_transitive … R (λ_.lex R) → R_transitive_req R →
       ∀L1,L2,T. L1 ⪤*[R,T] L2 →
       ∃∃L. L1 ⪤[CTC … R] L & L ≡[T] L2.
 #R #H1R #H2R #H3R #H4R #L1 #L2 #T #H
@@ -45,7 +47,7 @@ lapply (s_rs_transitive_lex_inv_isid … H3R) -H3R #H3R
 [ /4 width=3 by req_refl, lex_refl, inj, ex2_intro/
 | #L0 #L2 #_ #HL02 * #L * #f0 #Hf0 #HL1 #HL0
   lapply (req_rex_trans … HL0 … HL02) -L0 // * #f1 #Hf1 #HL2
-  elim (sex_sdj_split … ceq_ext … HL2 f0 ?) -HL2
+  elim (sex_sdj_split_sn … ceq_ext … HL2 f0 ?) -HL2
   [ #L0 #HL0 #HL02 |*: /2 width=1 by ext2_refl, sdj_isid_dx/ ]
   lapply (sex_sdj … HL0 f1 ?) /2 width=1 by sdj_isid_sn/ #H
   elim (frees_sex_conf_fsge … Hf1 … H) // -H2R -H #f2 #Hf2 #Hf21