os_cotransitive: cotransitive ? os_excess
}.
-interpretation "Ordered set excess" 'nleq a b =
- (cic:/matita/dama/ordered_set/os_excess.con _ a b).
+interpretation "Ordered set excess" 'nleq a b = (os_excess _ a b).
(* Definition 2.2 (3) *)
definition le ≝ λE:ordered_set.λa,b:E. ¬ (a ≰ b).
-interpretation "Ordered set greater or equal than" 'geq a b =
- (cic:/matita/dama/ordered_set/le.con _ b a).
+interpretation "Ordered set greater or equal than" 'geq a b = (le _ b a).
-interpretation "Ordered set less or equal than" 'leq a b =
- (cic:/matita/dama/ordered_set/le.con _ a b).
+interpretation "Ordered set less or equal than" 'leq a b = (le _ a b).
lemma le_reflexive: ∀E.reflexive ? (le E).
unfold reflexive; intros 3 (E x H); apply (os_coreflexive ?? H);
cases (os_cotransitive ??? b1 H) (H1 H1); [assumption]
cases (Lb1b H1);
qed.
-
-
\ No newline at end of file