proposition: Lemma cmΣ_negate (n : nat) (f : nat -> CR) : @cmΣ CRasCMonoid n (- f) = - @cmΣ CRasCMonoid n f.
proof: Proof. induction n as [| n IH]. - apply CRopp_0. - rewrite cmΣ_succ. transitivity ( (- f)%mc n + - @cmΣ CRasCMonoid n f)%CR. apply ucFun2_wd. reflexivity. exact IH. clear IH. change (- @cmΣ CRasCMonoid (S n) f) with (-(f n + @cmΣ CRasCMonoid n f))%CR. rewrite CRopp_plus_distr. reflexivity. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.reals.CRreal Coq.Unicode.Utf8 Coq.Program.Program CoRN.reals.fast.CRArith CoRN.reals.fast.CRabs CoRN.tactics.Qauto Coq.QArith.Qround CoRN.model.metric2.Qmetric CoRN.stdlib_omissions.P CoRN.stdlib_omissions.Z CoRN.stdlib_omissions.Q CoRN.stdlib_omissions.N CoRN.ode.metric CoRN.ode.FromMetric2 CoRN.ode.SimpleIntegration