What is the test for proving that a criminal offence has been committed?

The elements of a criminal offense may be proven by either direct or circumstantial evidence, or by inference. (People v. Cole (1985) 165 Cal.App.3d 41, 48, 211 Cal.Rptr. 242; see CALJIC 2.00.) "An inference is a deduction of fact that may logically and reasonably be drawn from another fact or group of facts found or otherwise established in the action." (Evid.Code, 600, subd. (b).) Thus, the specific inquiry here is whether it may logically and reasonably be deduced that appellant's prior convictions were "formally distinct, from filing," i.e., initiated by separate criminal complaints or indictments.