theorem tdeq_canc_dx: ∀h,o. right_cancellable … (tdeq h o).
/3 width=3 by tdeq_trans, tdeq_sym/ qed-.
-theorem tdeq_repl: â\88\80h,o,T1,T2. T1 â\89¡[h, o] T2 →
- â\88\80U1. T1 â\89¡[h, o] U1 â\86\92 â\88\80U2. T2 â\89¡[h, o] U2 â\86\92 U1 â\89¡[h, o] U2.
+theorem tdeq_repl: â\88\80h,o,T1,T2. T1 â\89\9b[h, o] T2 →
+ â\88\80U1. T1 â\89\9b[h, o] U1 â\86\92 â\88\80U2. T2 â\89\9b[h, o] U2 â\86\92 U1 â\89\9b[h, o] U2.
/3 width=3 by tdeq_canc_sn, tdeq_trans/ qed-.
(* Negated main properies ***************************************************)
-theorem tdeq_tdneq_trans: â\88\80h,o,T1,T. T1 â\89¡[h, o] T â\86\92 â\88\80T2. (T â\89¡[h, o] T2 → ⊥) →
- T1 â\89¡[h, o] T2 → ⊥.
+theorem tdeq_tdneq_trans: â\88\80h,o,T1,T. T1 â\89\9b[h, o] T â\86\92 â\88\80T2. (T â\89\9b[h, o] T2 → ⊥) →
+ T1 â\89\9b[h, o] T2 → ⊥.
/3 width=3 by tdeq_canc_sn/ qed-.
-theorem tndeq_tdeq_canc_dx: ∀h,o,T1,T. (T1 ≡[h, o] T → ⊥) → ∀T2. T2 ≡[h, o] T →
- T1 â\89¡[h, o] T2 → ⊥.
+theorem tdneq_tdeq_canc_dx: ∀h,o,T1,T. (T1 ≛[h, o] T → ⊥) → ∀T2. T2 ≛[h, o] T →
+ T1 â\89\9b[h, o] T2 → ⊥.
/3 width=3 by tdeq_trans/ qed-.