proposition: Lemma is_linear_scal_r (k : K) : (forall n m : K, mult n m = mult m n) -> is_linear (fun x : V => scal k x).
proof: Proof. split. - move => u v ; by apply @scal_distr_l. - move => u v /= ; apply sym_eq ; rewrite !@scal_assoc. by rewrite H. - exists (abs k + 1) ; split. apply Rplus_le_lt_0_compat. apply abs_ge_0. exact Rlt_0_1. move => x /=. rewrite Rmult_plus_distr_r Rmult_1_l -(Rplus_0_r (norm (scal k x))). apply Rplus_le_compat. apply norm_scal. apply norm_ge_0. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv