Does a prison official's deliberate indifference to a substantial risk of harm to an inmate violate the Eighth Amendment?

A prison official's deliberate indifference to a substantial risk of harm to an inmate violates the Eighth Amendment. Farmer v. Brennan, 511 U.S. at 828. To succeed on a claim of deliberate indifference to the threat of serious harm or injury by another prisoner, plaintiff must demonstrate that the deprivation of his rights was "objectively, sufficiently serious." Id. at 834. When the claim is predicated upon the failure to protect, the deprivation is deemed to be sufficiently serious if there was a substantial risk that the prisoner would suffer serious harm. Id. The prisoner must also demonstrate that the defendant had a "sufficiently culpable state of mind." Id. The prisoner must demonstrate that the defendant knew of and disregarded an excessive risk to his safety: "the official must both be aware of facts from which the inference could be drawn that a substantial risk of serious harm exists, and he must also draw the inference." Id. at 837.