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This report has been submitted forr publication outside of ITC and will probably be copyrighted if accepted for publication. It has been issued as a Technical Report forr early dissemination of its contents. In view of the transfert of copy right too the outside publisher, its distribution outside of ITC priorr to publication should be limited to peer… (More)

Enormous progress has been achieved in the last decade in the verification of timed systems, making it possible to analyze significant real-world protocols. An open challenge is the identification of fully symbolic verification techniques, able to deal effectively with the finite state component as well as with the timing aspects. In this paper we propose a… (More)

In this paper we introduce sets containing number-valued functions. Different arithmetic operations on maps between any set and such functional sets are later defined. The notation and terminology used here are introduced in the following papers: In this paper x, X, X 1 , X 2 are sets. Let Y be a functional set. The functor DOMS(Y) is defined by: (Def. 1)… (More)

This report has been submitted forr publication outside of ITC and will probably be copyrighted if accepted for publication. It has been issued as a Technical Report forr early dissemination of its contents. In view of the transfert of copy right too the outside publisher, its distribution outside of ITC priorr to publication should be limited to peer… (More)

In this article we demonstrate basic properties of the continuous functions from R to R n which correspond to state space equations in control engineering. The terminology and notation used here have been introduced in the following denote partial functions from R to R n , and h denotes a partial function from R to the carrier of E n , ·. Let us consider n,… (More)

In the article we prove that a family of open n-hypercubes is a basis of n-dimensional Euclidean space. The equality of the space and the product of n real lines has been proven. For simplicity, we use the following convention: x, y are sets, i, n are natural numbers, r, s are real numbers, and f 1 , f 2 are n-long real-valued finite sequences. Let s be a… (More)

In this paper we show the finite dimensionality of real linear spaces with their carriers equal R n. We also give the standard basis of such spaces. For the set R n we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal n. We use the following convention: i, j,… (More)

The collection of works for this special issue was inspired by the presentations given at the 2011 AMS Special Session on Formal Mathematics for Mathematicians: Developing Large Repositories of Advanced Mathematics. The issue features a collection of articles by practitioners of formalizing proofs who share a deep interest in making computerized mathematics… (More)