milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/feqg_fqus.ma b/matita/matita/contribs/lambdadelta/static_2/static/feqg_fqus.ma
index b2db044de0aad790092ce6a2a74af5670a93fecb..33663faa0c8ea76cacd9b5260883798b1ae47113 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/feqg_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/feqg_fqus.ma
@@ -19,6 +19,19 @@ include "static_2/static/feqg.ma".
 
 (* Properties with star-iterated structural successor for closures **********)
 
+lemma feqg_fquq_trans (S) (b):
+      reflexive … S → symmetric … S → Transitive … S →
+      ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ ⬂⸮[b] ❪G2,L2,T2❫ →
+      ∃∃G,L0,T0. ❪G1,L1,T1❫ ⬂⸮[b] ❪G,L0,T0❫ & ❪G,L0,T0❫ ≛[S] ❪G2,L2,T2❫.
+#S #b #H1S #H2S #H3S #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H2
+elim(feqg_inv_gen_dx … H1) -H1 // #HG #HL1 #HT1 destruct
+elim (reqg_fquq_trans … H2 … HL1) -L // #L #T0 #H2 #HT02 #HL2
+elim (teqg_fquq_trans … H2 … HT1) -T // #L0 #T #H2 #HT0 #HL0
+lapply (teqg_reqg_conf_sn … HT02 … HL0) -HL0 // #HL0
+/4 width=7 by feqg_intro_dx, reqg_trans, teqg_trans, ex2_3_intro/
+qed-.
+
 lemma feqg_fqus_trans (S) (b):
       reflexive … S → symmetric … S → Transitive … S →
       ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ →