renaming

[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..cbd1284cea26f1dd7566471736bb0cd922e28e34 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 +17,36 @@ 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-.
+
+(* Main inversion lemmas with degree-based equivalence on terms *************)
+
+theorem ffdeq_tdneq_repl_dx: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
+                             ∀U1,U2. ⦃G1, L1, U1⦄ ≛[h, o] ⦃G2, L2, U2⦄ →
+                             (T2 ≛[h, o] U2 → ⊥) → (T1 ≛[h, o] U1 → ⊥).
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #HT #U1 #U2 #HU #HnTU2 #HTU1
+elim (ffdeq_inv_gen_sn … HT) -HT #_ #_ #HT
+elim (ffdeq_inv_gen_sn … HU) -HU #_ #_ #HU
+/3 width=5 by tdeq_repl/
+qed-.