Is the accusatory pleading necessarily included in the statutory definition of the crime?

Thus, where the accusatory pleading is stated in the statutory definition of the crime, the lesser offense is necessarily included if the legal elements constituting the offense charged cannot be committed without necessarily committing the legal elements of a lesser offense as defined by statute. (People v. Francis, supra, 71 Cal.2d 66, 73, 75 Cal.Rptr. 199, 450 P.2d 591 ["to be necessarily included, the lesser offense must be 'part of the greater in fact' as well as being 'embraced within the legal definition of the greater as a part thereof.' "].)