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1,806
Finite Sequences and Tuples of Elements of a Nonempty Sets
, 1990
"... this article is the definition of tuples. The element of a set of all sequences of the length n of D is called a tuple of a nonempty set D and it is denoted by element of D ..."
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Cited by 332 (7 self)
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this article is the definition of tuples. The element of a set of all sequences of the length n of D is called a tuple of a nonempty set D and it is denoted by element of D
Inclusion Constraints over Nonempty Sets of Trees
, 1997
"... We present a new constraint system called INES. Its constraints are conjunctions of inclusions t1 `t2 between firstorder terms (without set operators) which are interpreted over nonempty sets of trees. The existing systems of set constraints can express INES constraints only if they include ne ..."
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Cited by 14 (5 self)
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We present a new constraint system called INES. Its constraints are conjunctions of inclusions t1 `t2 between firstorder terms (without set operators) which are interpreted over nonempty sets of trees. The existing systems of set constraints can express INES constraints only if they include
"directed, NDimensional, Concept Labels, NonEmpty Set,
"... this paper the authors see concept mapping is essentially a method to regulate the ratios between fragmentation/coherence and cognitiveoverhead /flexibility during the students' browsing in hyperlinked documents. They also propose that increasing the coherence criterion reduces the cognitive f ..."
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this paper the authors see concept mapping is essentially a method to regulate the ratios between fragmentation/coherence and cognitiveoverhead /flexibility during the students' browsing in hyperlinked documents. They also propose that increasing the coherence criterion reduces the cognitive flexibility, while decreasing the cognitive overhead brings along a higher risk of fragmentation. with a dynamic browsing. Not constructivist. The paper is concerned with the dynamics of mapping in a hypermedia environment. The authors write of a complex series of experiments that tackle the cognitive processes operating on learners. They equate the mapping environment withWWW/ hypermedia. Their unique contribution concerns a rulebased
Function domains and Frænkel operator
 Journal of Formalized Mathematics
, 1990
"... Summary. We deal with a non–empty set of functions and a non–empty set of functions from a set A to a non–empty set B. In the case when B is a non–empty set, B A is redefined. It yields a non–empty set of functions from A to B. An element of such a set is redefined as a function from A to B. Some th ..."
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Cited by 147 (18 self)
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Summary. We deal with a non–empty set of functions and a non–empty set of functions from a set A to a non–empty set B. In the case when B is a non–empty set, B A is redefined. It yields a non–empty set of functions from A to B. An element of such a set is redefined as a function from A to B. Some
Partial Functions
"... this article we prove some auxiliary theorems and schemes related to the articles: [1] and [2]. MML Identifier: PARTFUN1. WWW: http://mizar.org/JFM/Vol1/partfun1.html The articles [4], [6], [3], [5], [7], [8], and [1] provide the notation and terminology for this paper. We adopt the following rules ..."
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Cited by 492 (10 self)
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rules: x, y, y 1 , y 2 , z, z 1 , z 2 denote sets, P , Q, X , X 0 , X 1 , X 2 , Y , Y 0 , Y 1 , Y 2 , V , Z denote sets, and C, D denote non empty sets. We now state three propositions: (1) If P ` [: X 1
Partially Ordered Sets
, 2000
"... this article we define the choice function of a nonempty set family that does not contain ; as introduced in [6, pages 8889]. We define order of a set as a relation being reflexive, antisymmetric and transitive in the set, partially ordered set as structure nonempty set and order of the set, cha ..."
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Cited by 155 (4 self)
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this article we define the choice function of a nonempty set family that does not contain ; as introduced in [6, pages 8889]. We define order of a set as a relation being reflexive, antisymmetric and transitive in the set, partially ordered set as structure nonempty set and order of the set
On the nonemptiness of the fuzzy core ∗
"... The seminal contribution of DebreuScarf [4] connects the two concepts of core and competitive equilibrium in exchange economies. In effect, their coreequilibrium equivalence result states that, when the set of economic agents is replicated, the set of core allocations of the replica economy shrink ..."
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provide an elementary proof of the nonemptiness of the fuzzy core for an exchange economy. Unlike the classical DebreuScarf limit theorem [4] and its numerous extensions our result does not require any asymptotic intersectionor limit of the set of core allocations of replica economies.
The Reflection Theorem
 Journal of Formalized Mathematics
, 1990
"... this paper (and in another Mizar articles) we work in TarskiGrothendieck (TG) theory (see [17]) which ensures the existence of sets that have properties like universal class (i.e. this theory is stronger than MK). The sets are introduced in [15] and some concepts of MK are modeled. The concepts are ..."
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Cited by 249 (51 self)
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are: the class On of all ordinal numbers belonging to the universe, subclasses, transfinite sequences of nonempty elements of universe, etc. The reflection theorem states that if A ¸ is an increasing and continuous transfinite sequence of nonempty sets and class A =
Binary operations
 Journal of Formalized Mathematics
, 1989
"... Summary. In this paper we define binary and unary operations on domains. We also define the following predicates concerning the operations:... is commutative,... is associative,... is the unity of..., and... is distributive wrt.... A number of schemes useful in justifying the existence of the operat ..."
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Cited by 363 (6 self)
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〉). In the sequel A is a set. Let A, B be non empty sets, let C be a set, let f be a function from [:A, B:] into C, let a be an element of A, and let b be an element of B. Then f(a, b) is an element of C. The following proposition is true (2) 1 Let A, B, C be non empty sets and f1, f2 be functions from [:A, B
{EXPR,TERM,NAT,DIG}. {begin,end,case,of,if,then,else,while,do,repeat,until,for,to,downto}.
"... definition 1. An alphabet is a finite, nonempty set. The elements of an alphabet are called symbols. Alphabets are usually specified by enumeration. examples: {a, b}. ..."
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definition 1. An alphabet is a finite, nonempty set. The elements of an alphabet are called symbols. Alphabets are usually specified by enumeration. examples: {a, b}.
Results 1  10
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