  This paper introduces a uniform substitution calculus for differential
refinement logic dRL. The logic dRL extends the differential dynamic logic dL
such that one can simultaneously reason about properties of and relations
between hybrid systems. Refinements are useful e.g. for simplifying proofs by
relating a concrete hybrid system to an abstract one from which the property
can be proved more easily. Uniform substitution is the key to parsimonious
prover microkernels. It enables the verbatim use of single axiom formulas
instead of axiom schemata with soundness-critical side conditions scattered
across the proof calculus. The uniform substitution rule can then be used to
instantiate all axioms soundly. Access to differential variables in dRL enables
more control over the notion of refinement, which is shown to be decidable on a
fragment of hybrid programs.
