dARL supplies a sound deductive refinement calculus with trace semantics for verifying and simplifying differential-algebraic programs, shown complete for index reduction certification.
By the Mean Value Theorem (Theorem 3), there exists aξ∈(0, T φ)such that: φ(Tφ)JeK=T φ d dt φ(ξ)JeK+φ(0)JeK
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A Deductive Refinement Calculus for Differential-Algebraic Programs
dARL supplies a sound deductive refinement calculus with trace semantics for verifying and simplifying differential-algebraic programs, shown complete for index reduction certification.