proposition: Theorem mulℝ_Cauchy_realizer : forall e, mulℝ_Cauchy↓e ⊩ ∀x y, Cauchy x → Cauchy y → Cauchy (x * y)%Re.
proof: Proof. intro e. startn 0. apply mulℝ_proper_realizer. unfold Cauchy in *. do 4 eexists. split. eok. split; eok. Qed.
imports: QArith Psatz ClassicalRealizability.Kbase ClassicalRealizability.Rationals ClassicalRealizability.Real_definitions ClassicalRealizability.Real_relations