Complex zero strip decreasing operators

In this paper we study the effect of linear differential operators coming from the Laguerre-Polya class that act on functions in the extended Laguerre-Polya class with zeros in a horizontal strip in the complex plane. These operator decrease the size of the strip containing the zeros.Comment: 17 pages, corrected several typos, added a citation. appears in Math. Anal. Appl. (2015

Hipster: Integrating Theory Exploration in a Proof Assistant

This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can be used in two main modes. The first is exploratory mode, used for automatically generating basic lemmas about a given set of datatypes and functions in a new theory development. The second is proof mode, used in a particular proof attempt, trying to discover the missing lemmas which would allow the current goal to be proved. Hipster's proof mode complements and boosts existing proof automation techniques that rely on automatically selecting existing lemmas, by inventing new lemmas that need induction to be proved. We show example uses of both modes