X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsyntax%2Ftdeq_tdeq.ma;h=80d13f4e6cbcbe45f088ea698747ff6b4d69a14f;hp=39b06145cd3706f2c5438b48fe4001d1bc1c7ecd;hb=222044da28742b24584549ba86b1805a87def070;hpb=b4b5f03ffca4f250a1dc02f277b70e4f33ac8a9b

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_tdeq.ma
index 39b06145c..80d13f4e6 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_tdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_tdeq.ma
@@ -24,7 +24,27 @@ theorem tdeq_trans: ∀h,o. Transitive … (tdeq h o).
   elim (tdeq_inv_sort1_deg … H … Hs) -s /2 width=3 by tdeq_sort/
 | #i1 #i #H <(tdeq_inv_lref1 … H) -H //
 | #l1 #l #H <(tdeq_inv_gref1 … H) -H //
-| #I #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H destruct
+| #I #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H
   elim (tdeq_inv_pair1 … H) -H /3 width=1 by tdeq_pair/
 ]
 qed-.
+
+theorem tdeq_canc_sn: ∀h,o. left_cancellable … (tdeq h o).
+/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
+
+theorem tdeq_canc_dx: ∀h,o. right_cancellable … (tdeq h o).
+/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
+
+theorem tdeq_repl: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
+                   ∀U1. T1 ≛[h, o] U1 → ∀U2. T2 ≛[h, o] U2 → U1 ≛[h, o] U2.
+/3 width=3 by tdeq_canc_sn, tdeq_trans/ qed-.
+
+(* Negated main properies ***************************************************)
+
+theorem tdeq_tdneq_trans: ∀h,o,T1,T. T1 ≛[h, o] T → ∀T2. (T ≛[h, o] T2 → ⊥) →
+                          T1 ≛[h, o] T2 → ⊥.
+/3 width=3 by tdeq_canc_sn/ qed-.
+
+theorem tdneq_tdeq_canc_dx: ∀h,o,T1,T. (T1 ≛[h, o] T → ⊥) → ∀T2. T2 ≛[h, o] T →
+                            T1 ≛[h, o] T2 → ⊥.
+/3 width=3 by tdeq_trans/ qed-.