How have courts interpreted the words "clearly proved" and "beyond a reasonable doubt"?

In 1881, California joined the jurisdictions that equated the words "clearly proved," as used in M'Naghten, with "beyond a reasonable doubt," when this court decided People v. Wreden (1881) 59 Cal. 392. In that case, the defendant, who was charged with murder, asserted the defense of insanity. The trial court instructed the jury that " 'insanity must be clearly established by satisfactory proof....' " (Id. at p. 395, italics omitted.) On appeal, we held that the instruction was tantamount to telling the jury that the defendant must show insanity beyond a reasonable doubt, and that it was therefore erroneous. We observed: "In a late case (People v. Wilson [1874] 49 Cal. 13), it was held to be well settled ... that insanity ... need not be proved beyond a reasonable doubt, but that it might be established 'by mere preponderating evidence.' Is not the expression 'clearly established by satisfactory proof ' the full equivalent of 'established by satisfactory proof beyond a reasonable doubt'? How can a fact be said to be clearly established so long as there is a reasonable doubt whether it has been established at all? [p] There can be no 'reasonable doubt' of a fact after it has been clearly established by satisfactory proof." (People v. Wreden, supra, 59 Cal. at p. 395.)