update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / ffdeq_ffdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/ffdeq_ffdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/ffdeq_ffdeq.ma
index 46400a913bda632975febee4dc8ec5950fd7c928..40a805259638e00110e6e0823d9b1333309e904e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/ffdeq_ffdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/ffdeq_ffdeq.ma
@@ -17,17 +17,25 @@ include "basic_2/static/ffdeq.ma".
 
 (* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
 
+(* Advanced properties ******************************************************)
+
+lemma ffdeq_sym: ∀h,o. tri_symmetric … (ffdeq h o).
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1
+/3 width=1 by ffdeq_intro_dx, lfdeq_sym, tdeq_sym/
+qed-.
+
 (* Main properties **********************************************************)
 
 theorem ffdeq_trans: ∀h,o. tri_transitive … (ffdeq h o).
 #h #o #G1 #G #L1 #L #T1 #T * -G -L -T
-#L #HL1 #G2 #L2 #T2 * -G2 -L2 -T2 /3 width=3 by ffdeq_intro, lfdeq_trans/
+#L #T #HL1 #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
+/4 width=5 by ffdeq_intro_sn, lfdeq_trans, tdeq_lfdeq_div, tdeq_trans/
 qed-.
 
 theorem ffdeq_canc_sn: ∀h,o,G,G1,G2,L,L1,L2,T,T1,T2.
-                       â¦\83G, L, Tâ¦\84 â\89¡[h, o] â¦\83G1, L1, T1â¦\84â\86\92 â¦\83G, L, Tâ¦\84 â\89¡[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89¡[h, o] ⦃G2, L2, T2⦄.
+                       â¦\83G, L, Tâ¦\84 â\89\9b[h, o] â¦\83G1, L1, T1â¦\84â\86\92 â¦\83G, L, Tâ¦\84 â\89\9b[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] ⦃G2, L2, T2⦄.
 /3 width=5 by ffdeq_trans, ffdeq_sym/ qed-.
 
 theorem ffdeq_canc_dx: ∀h,o,G1,G2,G,L1,L2,L,T1,T2,T.
-                       â¦\83G1, L1, T1â¦\84 â\89¡[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G2, L2, T2â¦\84 â\89¡[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89¡[h, o] ⦃G2, L2, T2⦄.
+                       â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G2, L2, T2â¦\84 â\89\9b[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] ⦃G2, L2, T2⦄.
 /3 width=5 by ffdeq_trans, ffdeq_sym/ qed-.