Here φ and ψ are any schemata and Γ is a (possibly empty) set of schemata. The Deduction Theorem, we shall see, is a very nice feature of an axiomatic system, for it allows one to discover theorems much more readily than ordinarily is possible by building actual proofs. Its true value lies elsewhere than in efficiency, though. At the end of this note we will discuss the importance of the Deduct...

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

The normalization theorem for the system of extended natural deduction will be proved as a consequence of the cut-elimination theorem, by using the connections between the system of extended natural deduction and a standard system of sequents.

Deduction modulo is a theoretical framework designed to introduce computational steps in deductive systems. This approach is well suited to automated theorem proving and a tableau method for firstorder classical deduction modulo has been developed. We reformulate this method and give an (almost constructive) semantic completeness proof. This new proof allows us to extend the completeness theore...

In this paper, we show how a system for automated deduction can be given computational reeection, i.e. can aaect its own computation mechanism, by using the very same machinery implementing logical deduction. This feature, that we call computational reeection via mechanized logical deduction, provides both theoretical and practical advantages. First, the theorem prover can inspect, extend and m...

We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of real and finite square $A$ (and complex ones also). The elementary method developed avoids Jordan canonical form, eigenvectors, resolution any linear system, inversion, polynomial interpolation, integration, functional analysis, generalized Fibonacci sequences. basic tools are Cayley-Hamilton theore...

In this paper, after reviewing some results in minimal space, some new results in this setting are given. We prove a generalized form of the Fan-KKM typetheorem in minimal vector spaces. As some applications, the open type of matching theorem and generalized form of the classical KKM theorem in minimal vector spaces are given.