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We present a framework for (static) verification of general resource usage program properties. The framework extends the criteria of correctness as the conformance of a program to a specification expressing non-functional global properties, such as upper and lower bounds on execution time, memory, energy, or user defined resources, given as functions on input data sizes. A given specification can include both lower and upper bound resource usage functions, i.e., it can express intervals where the resource usage is supposed to be included in. We have defined an abstract semantics for resource usage properties and operations to compare the (approximated) intended semantics of a program (i.e., the specification) with approximated semantics inferred by static analysis. These operations include the comparison of arithmetic functions (e.g., polynomial, exponential or logarithmic functions). A novel aspect of our framework is that the static checking of assertions generates answers that include conditions under which a given specification can be proved or disproved. For example, these conditions can express intervals of input data sizes such that a given specification can be proved for some intervals but disproved for others. We have implemented our techniques within the Ciao/CiaoPP system in a natural way, so that the novel resource usage verification blends in with the CiaoPP framework that unifies static verification and static debugging (as well as run-time verification and unit testing).