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We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an O(1)-competitive algorithm. For a monotone subadditive objective function over an arbitrary downward-closed feasibility constraint, we give an O( n ^2 r)-competitive algorithm (where r is the cardinality of the largest feasible subset). Inspired by the proof of our subadditive prophetarXiv:1611.00665v1 fatcat:qdks4q6gq5fr7dc7wocdlllckm