Zachary A. Smith appeals the judgment of the Bankruptcy Appellate Panel (BAP) affirming the bankruptcy court’s 1 order denying his motion for contempt for violation of his discharge injunction.

Smith is an inmate of the Missouri Department of Corrections serving a life sentence with no possibility of parole. On January 20, 2009, the State obtained a judgment against him under the Missouri Incarceration Reimbursement Act (MIRA), Mo.Rev.Stat. §§ 217.825-217.841, for the costs of his incarceration: judgment was entered for costs of $87,830.13 through March 26, 2007, and for costs after that date through his final release, with future costs evidenced by a Treasurer’s Certificate of Costs. The judgment directed the inmate treasurer to forward to the State 90% of all deposits to Smith’s account, excluding wages and bonuses earned while incarcerated. Smith filed a chapter 7 bankruptcy petition on September 14, 2010; he received a discharge in March 2011, and the case was closed in July. In September 2012, the inmate treasurer directed $45 from Smith’s account to the State pursuant to the MIRA judgment. Smith filed a motion for contempt in the bankruptcy court, alleging his creditors were violating the discharge order. The court denied the motion, finding that there had been no violation of the discharge injunction because bankruptcy law does not allow a discharge of future debts, and the MIRA judgment was still valid as to future reimbursement. The BAP affirmed on appeal. Smith appeals, arguing that the MIRA judgment is void based on the recent Missouri Court of Appeals decision in State ex rel. Koster v. Cowin, 390 S.W.3d 239 (Mo.Ct.App. 2013) (judgment under MIRA permits reimbursement only from assets to which inmate has present legal right); and that MIRA violates the Supremacy Clause.

Upon careful consideration, see In re Ungar, 633 F.3d 675, 678-79 (8th Cir. 2011) (standard of review), this court affirms. First, Smith’s argument that the MIRA judgment is invalid is barred by the Rook- *617 er-Feldman 2 doctrine. See Exxon Mobil Corp. v. Saudi Basic Indus. Corp., 544 U.S. 280, 284, 125 S.Ct. 1517, 161 L.Ed.2d 454 (2005) (Rooker-Feldman doctrine is limited to cases brought by state-court losers complaining of injuries caused by state-court judgments rendered before district court proceedings were commenced and inviting district court review and rejection of those judgments); Skit Int'l, Ltd. v. DAC Techs. of Ark., Inc., 487 F.3d 1154, 1156-57 (8th Cir. 2007) (Rooker-Feldman doctrine prohibits lower federal courts from exercising appellate review of state-court judgments). Second, this court agrees with the bankruptcy court that the costs of Smith’s incarceration after September 2010 accrued post-petition, as Smith remained incarcerated, and thus the debt is not dischargeable. See Bush v. Taylor, 912 F.2d 989, 993 (8th Cir. 1990) (en banc) (post-petition debts are not dis-chargeable in bankruptcy). Finally, this court rejects Smith’s argument that MIRA violates the Supremacy Clause. See Sears, Roebuck & Co. v. O'Brien, 178 F.3d 962, 966 (8th Cir. 1999) (criteria for finding Supremacy Clause violation).

The judgment of the BAP is affirmed.