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Manysorted sets
 Journal of Formalized Mathematics
, 1993
"... Summary. The article deals with parameterized families of sets. When treated in a similar way as sets (due to systematic overloading notation used for sets) they are called many sorted sets. For instance, if x and X are two manysorted sets (with the same set of indices I) then relation x ∈ X is def ..."
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Cited by 195 (23 self)
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Summary. The article deals with parameterized families of sets. When treated in a similar way as sets (due to systematic overloading notation used for sets) they are called many sorted sets. For instance, if x and X are two manysorted sets (with the same set of indices I) then relation x ∈ X is defined as ∀i∈Ixi ∈ Xi. I was prompted by a remark in a paper by Tarlecki and Wirsing: “Throughout the paper we deal with manysorted sets, functions, relations etc.... We feel free to use any standard settheoretic notation without explicit use of indices ” [6, p. 97]. The aim of this work was to check the feasibility of such approach in Mizar. It works. Let us observe some peculiarities: empty set (i.e. the many sorted set with empty set of indices) belongs to itself (theorem 133), we get two different inclusions X ⊆ Y iff ∀i∈IXi ⊆ Yi and X ⊑ Y iff ∀xx ∈ X ⇒ x ∈ Y equivalent only for sets that yield non empty values. Therefore the care is advised.
On the Decomposition of the States of SCM
, 1993
"... This article continues the development of the basic terminology ..."
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Cited by 52 (1 self)
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This article continues the development of the basic terminology
Bounding boxes for compact sets inE 2
 Journal of Formalized Mathematics
, 1997
"... Summary. We define pseudocompact topological spaces and prove that every compact space is pseudocompact. We also solve an exercise from [14] p.225 that for a topological space X the following are equivalent: • Every continuous real map from X is bounded (i.e. X is pseudocompact). • Every continuous ..."
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Cited by 39 (2 self)
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Summary. We define pseudocompact topological spaces and prove that every compact space is pseudocompact. We also solve an exercise from [14] p.225 that for a topological space X the following are equivalent: • Every continuous real map from X is bounded (i.e. X is pseudocompact). • Every continuous real map from X attains minimum. • Every continuous real map from X attains maximum. Finally, for a compact set in E 2 we define its bounding rectangle and introduce a collection of notions associated with the box.
Constant assignment macro instructions of SCMFSA
 Part II. Journal of Formalized Mathematics
, 1996
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Minimal Signature for Partial Algebra
 Journal of Formalized Mathematics
, 1995
"... this paper. ..."
The SCMPDS computer and the basic semantics of its instructions
 Journal of Formalized Mathematics
, 1999
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Conditional branch macro instructions of SCMFSA
 Part I. Journal of Formalized Mathematics
, 1996
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The construction and computation of conditional statements for SCMPDS
 Journal of Formalized Mathematics
, 1999
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