update in staic_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / rex_lex.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma
index 9329d7f84c7704c87bcc840b16f430ccbd3d9d8c..c407319412c78b9c5a041e5312f8f486cd4bae56 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma
@@ -29,12 +29,28 @@ qed.
 
 (* Inversion lemmas with generic extension of a context sensitive relation **)
 
-lemma rex_inv_lex_req (R):
+lemma rex_inv_req_lex (R):
+      c_reflexive … R → f_confluent1_next R ceq →
+      ∀L1,L2,T. L1 ⪤[R,T] L2 →
+      ∃∃L. L1 ≡[T] L & L ⪤[R] L2.
+#R #H1R #H2R #L1 #L2 #T * #f1 #Hf1 #HL
+elim (sex_sdj_split_dx … ceq_ext … HL 𝐈𝐝) -HL
+[ #L0 #HL10 #HL02
+  lapply (sex_sdj … HL02 f1 ?) /2 width=1 by sdj_isid_sn/ #H
+  /3 width=5 by (* 2x *) ex2_intro/
+|*: /2 width=1 by ext2_refl, sdj_isid_dx/
+  #g #I #K #n #HLK #Hg @H2R /width=7 by/ (**) (* no auto with H2R *)
+]
+qed-.
+
+(* Forward lemmas with generic extension of a context sensitive relation **)
+
+lemma rex_fwd_lex_req (R):
       c_reflexive … R → rex_fsge_compatible R →
       ∀L1,L2,T. L1 ⪤[R,T] L2 →
       ∃∃L. L1 ⪤[R] L & L ≡[T] L2.
 #R #H1R #H2R #L1 #L2 #T * #f1 #Hf1 #HL
-elim (sex_sdj_split … ceq_ext … HL 𝐈𝐝 ?) -HL
+elim (sex_sdj_split_sn … ceq_ext … HL 𝐈𝐝 ?) -HL
 [ #L0 #HL10 #HL02 |*: /2 width=1 by ext2_refl, sdj_isid_dx/ ] -H1R
 lapply (sex_sdj … HL10 f1 ?) /2 width=1 by sdj_isid_sn/ #H
 elim (frees_sex_conf_fsge … Hf1 … H) // -H2R -H #f0 #Hf0 #Hf01