proposition: Lemma filterdiff_mult_fct {K : AbsRing} {U : NormedModule K} (f g : U -> K) x (lf lg : U -> K) : (forall (n m : K), mult n m = mult m n) -> filterdiff f (locally x) lf -> filterdiff g (locally x) lg -> filterdiff (fun t => mult (f t) (g t)) (locally x) (fun t => plus (mult (lf t) (g x)) (mult (f x) (lg t))).
proof: Proof. intros. by apply @filterdiff_scal_fct. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv