The following excerpt is from Martin v. Allison, No. 2:11-cv-0870 LKK GGH (HC) (E.D. Cal. 2014):
11. However, in a non-capital case, unless the failure to instruct on a lesser offense disregarded a defendant's theory of the case, no federal due process claim exists. See Solis v. Garcia, 219 F.3d 922, 929 (9th Cir. 2000). Here, petitioner's theory of the case is that "he was not there" when the crimes were committed, not that he killed in imperfect self-defense. He would be unable to state a due process failure to instruct claim in the context of this case.
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