partial commit in static_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 d031d93c40aefb5dc4d595e70cc67f99c3a764e6..3fb780bb8159b0d91f367a749d90ea55405184e6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma
@@ -20,22 +20,39 @@ include "static_2/static/req.ma".
 
 (* Properties with generic extension of a context-sensitive relation ********)
 
-lemma rex_lex: ∀R,L1,L2. L1 ⪤[R] L2 → ∀T. L1 ⪤[R,T] L2.
+lemma rex_lex (R):
+      ∀L1,L2. L1 ⪤[R] L2 → ∀T. L1 ⪤[R,T] L2.
 #R #L1 #L2 * #f #Hf #HL12 #T
 elim (frees_total L1 T) #g #Hg
-/4 width=5 by sex_sdj, sdj_isid_sn, ex2_intro/
+/4 width=5 by sex_sdj, pr_sdj_isi_sn, ex2_intro/
 qed.
 
 (* Inversion lemmas with generic extension of a context sensitive relation **)
 
-lemma rex_inv_lex_req: ∀R. c_reflexive … R →
-                       rex_fsge_compatible R →
-                       ∀L1,L2,T. L1 ⪤[R,T] L2 →
-                       ∃∃L. L1 ⪤[R] L & L ≡[T] L2.
+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 … 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 … Hf1 … H) // -H2R -H #f0 #Hf0 #Hf01
+elim (sex_sdj_split_dx … ceq_ext … HL 𝐢) -HL
+[ #L0 #HL10 #HL02
+  lapply (sex_sdj … HL02 f1 ?) /2 width=1 by pr_sdj_isi_sn/ #H
+  /3 width=5 by (* 2x *) ex2_intro/
+|*: /2 width=1 by ext2_refl, pr_sdj_isi_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_sn … ceq_ext … HL 𝐢 ?) -HL
+[ #L0 #HL10 #HL02 |*: /2 width=1 by ext2_refl, pr_sdj_isi_dx/ ] -H1R
+lapply (sex_sdj … HL10 f1 ?) /2 width=1 by pr_sdj_isi_sn/ #H
+elim (frees_sex_conf_fsge … Hf1 … H) // -H2R -H #f0 #Hf0 #Hf01
 /4 width=7 by sle_sex_trans, (* 2x *) ex2_intro/
 qed-.