proposition: Lemma plus_mono_bi : forall alpha beta gamma delta, alpha <= gamma -> beta < delta -> alpha + beta < gamma + delta.
proof: Proof. intros alpha beta gamma delta H H0; apply le_lt_trans with (gamma+beta). now apply plus_mono_weak_l. now apply plus_mono_r. Qed.
imports: Coq(Arith Logic.Epsilon Ensembles) ZornsLemma(CountableTypes)