proposition: Theorem le_epsilon_zero : forall (a : A), (forall (epsilon : A), ~eq epsilon zero -> le a epsilon) -> eq a zero.
proof: Proof. intuition. destruct (eq_dec a zero). trivial. exfalso. specialize (H (half a)). apply f. eapply le_half. apply H. eapply half_nz. trivial. Qed.
imports: Arith FCF.Fold List FCF.StdNat FCF.Rat