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We present several steps towards large formal mathematical wikis. The Coq proof assistant together with the CoRN repository are added to the pool of systems handled by the general wiki system described in [10]. A smart re-verification scheme for the large formal libraries in the wiki is suggested for Mizar/MML and Coq/CoRN, based on recently developed(More)
Formal mathematics has so far not taken full advantage of ideas from collaborative tools such as wikis and distributed version control systems (DVCS). We argue that the field could profit from such tools, serving both newcomers and experts alike. We describe a preliminary system for such collaborative development based on the Git DVCS. We focus, initially,(More)
Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. This work develops learning-based premise selection in two ways. First, a fine-grained dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise(More)
First-order translations of large mathematical repositories allow discovery of new proofs by automated reasoning systems. Large amounts of available mathematical knowledge can be re-used by combined AI/ATP systems, possibly in unexpected ways. But automated systems can be also more easily mis-led by irrelevant knowledge in this setting, and finding deeper(More)
Two methods for extracting detailed formal dependencies from the Coq and Mizar system are presented and compared. The methods are used for dependency extraction from two large mathematical repositories: the Coq Repository at Nijmegen and the Mizar Mathematical Library. Several applications of the detailed dependency analysis are described and proposed.(More)
The rank+nullity theorem states that, if T is a linear transformation from a finite-dimensional vector space V to a finite-dimensional vector space W , then dim(V) = rank(T) + nullity(T), where rank(T) = dim(im(T)) and nullity(T) = dim(ker(T)). The proof treated here is standard; see, for example , [14]: take a basis A of ker(T) and extend it to a basis B(More)
The Mizar Mathematical Library (MML) is a large corpus of formalised mathematical knowledge. It has been constructed over the course of many years by a large number of authors and maintainers. Yet the legal status of these efforts of the Mizar community has never been clarified. In 2010, after many years of loose deliberations, the community decided to(More)
In some theory development tasks, a problem is satisfactorily solved once it is shown that a theorem (conjecture) is derivable from the background theory (premises). Depending on one's motivations, the details of the derivation of the conjecture from the premises may or may not be important. In some contexts, though, one wants more from theory development(More)
For each set X, the power set of X forms a vector space over the field Z2 (the two-element field {0, 1} with addition and multiplication done modulo 2): vector addition is disjoint union, and scalar multiplication is defined by the two equations (1 · x := x, 0 · x := ∅ for subsets x of X). See [10], Exercise 2.K, for more information. Let S be a 1-sorted(More)