Does a failure to instruct a jury to convict a defendant of simple assault and battery constitute harmless error?

The failure to instruct on a lesser included offense supported by the evidence may be deemed harmless error if " 'the factual question posed by the omitted instruction was necessarily resolved adversely to the defendant under other, properly given instructions....' [Citations.]" (People v. Turner, supra, 50 Cal.3d at pp. 690-691, 268 Cal.Rptr. 706, 789 P.2d 887; People v. Ramkeesoon (1985) 39 Cal.3d 346, 351-352, 216 Cal.Rptr. 455, 702 P.2d 613.) No such implied finding can be located here. Convictions of simple assault and battery do not necessarily imply findings of violence or menace. Indeed, the acquittal on aggravated assault suggests the jury had doubts as to the degree of force used and might have convicted only of misdemeanor false imprisonment had it not been presented with the " 'unwarranted all-or-nothing choice' " (People v. Ramkeesoon, supra, at p. 352, 216 Cal.Rptr. 455, 702 P.2d 613) between conviction of the felony and complete acquittal on the charge.