partial commit in static_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 4ac00b7a1115b4d47726c2490281c04dc1f2b424..39059adfcf3acb5d75d060c36f6dea0d8abb05ae 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
@@ -13,44 +13,44 @@
 (**************************************************************************)
 
 include "static_2/relocation/lex_tc.ma".
-include "static_2/static/req_fqup.ma".
-include "static_2/static/req_fsle.ma".
+include "static_2/static/reqg_fqup.ma".
+include "static_2/static/req_req.ma".
 include "static_2/i_static/rexs_fqup.ma".
 
 (* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
 
 (* Properties with generic extension of a context sensitive relation ********)
 
-lemma rexs_lex: ∀R. c_reflexive … R →
-                ∀L1,L2,T. L1 ⪤[CTC … R] L2 → L1 ⪤*[R, T] L2.
+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 →
-                    ∀L1,L. L1 ⪤[CTC … R] L → ∀L2,T. L ≡[T] L2 →
-                    L1 ⪤*[R, T] L2.
+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.
 
 (* Inversion lemmas with generic extension of a context sensitive relation **)
 
 (* 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 →
-                        ∀L1,L2,T. L1 ⪤*[R, T] L2 →
-                        ∃∃L. L1 ⪤[CTC … R] L & L ≡[T] L2.
+lemma rexs_inv_lex_req (R):
+      c_reflexive … R → rex_fsge_compatible 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
 lapply (s_rs_transitive_lex_inv_isid … H3R) -H3R #H3R
 @(rexs_ind_sn … H1R … H) -H -L2
-[ /4 width=3 by req_refl, lex_refl, inj, ex2_intro/
+[ /4 width=3 by reqg_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
-  [ #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 … Hf1 … H) // -H2R -H #f2 #Hf2 #Hf21
+  elim (sex_sdj_split_sn … ceq_ext … HL2 f0 ?) -HL2
+  [ #L0 #HL0 #HL02 |*: /2 width=1 by ext2_refl, pr_sdj_isi_dx/ ]
+  lapply (sex_sdj … HL0 f1 ?) /2 width=1 by pr_sdj_isi_sn/ #H
+  elim (frees_sex_conf_fsge … Hf1 … H) // -H2R -H #f2 #Hf2 #Hf21
   lapply (sle_sex_trans … HL02 … Hf21) -f1 // #HL02
   lapply (sex_co ?? cfull (CTC … (cext2 R)) … HL1) -HL1 /2 width=1 by ext2_inv_tc/ #HL1
   /8 width=11 by sex_inv_tc_dx, sex_tc_dx, sex_co, ext2_tc, ext2_refl, step, ex2_intro/ (**) (* full auto too slow *)