In a collateral habeas review of a state conviction, is the reasonable doubt standard applied specifically?

Of those cases prior to Cage that involved collateral habeas review of state convictions, some did reverse the challenged convictions because of defects in the state trial court's instructions, as evaluated under the Winship standard. See, e.g., Ramirez v. Jones, 683 F.2d 712, 715 (2d Cir. 1982) (instructions shifted burden of proof to defendant on issue of intent). But petitioner has brought no cases to our attention that reversed state convictions specifically because of a defect in the state trial court's definition of the reasonable doubt standard.