In formal proof checking environments such as Mizar it is not merely the validity of mathematical formulas that is evaluated in the process of adoption to the body of accepted formalizations, butâ€¦ (More)

The existing examples of natural deduction proofs, either declarative or procedural, indicate that often the legibility of proof scripts is of secondary importance to the authors. As soon as theâ€¦ (More)

In this paper we explore the possibility of emulating the Mizar environment as close as possible inside the Isabelle logical framework. We introduce adaptations to the Isabelle/FOL object logic thatâ€¦ (More)

In this paper I present selected properties of triangular matrices and basic properties of the rank of matrices over a field. I define a submatrix as a matrix formed by selecting certain rows andâ€¦ (More)

Proof development in proof assistants such as HOL, Coq, Mizar, etc. is an activity where authors usually produce proofs by typing out proof scripts or system tactics. Quite frequently, however,â€¦ (More)

We continue Mizar formalization of general topology according to the book [16] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalizationâ€¦ (More)

In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affineâ€¦ (More)