proposition: Lemma ing_One : inject_Q ([1]:F) [=] [1].
proof: Proof. apply not_ap_imp_eq; intro H. elim H; intro Hlt; elim Hlt; intros N HN; elim HN; clear H Hlt HN; intros e He HN; simpl in HN. apply (less_irreflexive_unfolded F [0]). apply less_leEq_trans with e; auto. astepr ([1][-] ([1]:F)); eauto. apply (less_irreflexive_unfolded F [0]). apply less_leEq_trans with e; auto. astepr ([1][-] ([1]:F)); eauto. Qed.
imports: CoRN.algebra.Cauchy_COF CoRN.reals.CReals