This paper presents on-going researches on theoretical and practical issues of combining rewriting based automated theorem proving and user-guided proof development, with the strong constraint of safe cooperation of both. In practice, we instantiate the theoretical study on the Coq proof assistant and the ELAN rewriting based system, focusing first on equational and then on inductive proofs. Di...

Survivable systems are modelled abstractly as collections of services supported by any of a set of configurations of components. Reconfiguration to restore services as a result of component failure is viewed as a kind of “flow” analogous to information flow. We apply Meadows’ theorem on datset aggregates to characterize the maximum safe flow policy. For reconfiguration, safety means that servic...

Integrating decision procedures in proof assistants in a safe way is a major challenge. In this paper, we describe how, starting from Hilbert’s Nullstellensatz theorem, we combine a modified version of Buchberger’s algorithm and some reflexive techniques to get an effective procedure that automatically produces formal proofs of theorems in geometry. The method is implemented in the Coq system b...

We present the first next-to-next-to-leading logarithmic resummation for the two-jet rate in ee annihilation in the Durham and Cambridge algorithms. The results are obtained by extending the ARES method to observables involving any global, recursively infrared and collinear safe jet algorithm in ee collisions. As opposed to other methods, this approach does not require a factorization theorem f...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the...

Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

in this paper is introduced a new type of generalization of metric spaces called sb metric space. for this new kind of spaces it has been proved a common xed point theorem for four mappings which satisfy generalized contractive condition. we also present example to conrm our theorem.

the purpose of this article is to use the classical sampling theorem, wks sampling theorem, to deriveapproximate values of the eigenvalues of the sturm-liouville problems with eigenparameter in the boundaryconditions. error analysis is used to give estimates of the associated error. higher order approximations are also drived, which lead to more complicated computations. we give some examples a...