+
+(* 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-.