Improving Mizar Texts with Properties and Requirements

2015

J Autom Reasoning

The MIZAR VERIFIER uses definitional expansions for controlling proof structures. In this paper we propose another use of definitional expansions-enriching verified inferences by expansions of definitions of formulae included in the inferences and increasing the number of premises accessible by CHECKER. This introduces more knowledge to the reasoning, which helps to draw more conclusions. Some statistics about influence of such expansions on the MIZAR MATHEMATICAL LIBRARY are presented.

Section: Definitions and Redefinitions In Mizarmentioning

confidence: 99%

Definitional Expansions in Mizar

2015

J Autom Reasoning

“…Another type of possible reductions are facts processed by the mechanism called requirements, which are special modules implemented in the system for automatization of reasonings within particular theories, like arithmetic over complex numbers, [8]. An example of such reductions is complex multiplication by zero (z * 0 = 0, requirements ARITHM).…”

Section: Requirements-like Reductionsmentioning

confidence: 99%

On Rewriting Rules in Mizar

2012

J Autom Reasoning

“…Mizar allows registering various properties of predicates and functors [14] when defining new notions. Let us briefly recall that the set of currently implemented properties includes involutiveness and projectivity for unary operations, as well as commutativity and idempotence for binary operations.…”

Section: Introductionmentioning

confidence: 99%

Introducing Euclidean Relations to Mizar

Naumowicz

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

2017

Self Cite

Abstract-In this paper we present the methodology of implementing a new enhancement of the Mizar proof checker based on enabling special processing of Euclidean predicates, i.e. binary predicates which fulfill a specific variant of transitivity postulated by Euclid. Typically, every proof step in formal mathematical reasoning is associated with a formula to be proved and a list of references used to justify the formula. With the proposed enhancement, the Euclidean property of given relations can be registered during their definition, and so the verification of some proof steps related to these relations can be automated to avoid explicit referencing.