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Posterior Probability on Finite Set

distribution. Formalized Mathematics , 17( 2 ):173-178, 2009, doi: 10.2478/v10037-009-0020-z. [15] Hiroyuki Okazaki and Yasunari Shidama. Probability on finite set and real-valued random variables. Formalized Mathematics , 17( 2 ):129-136, 2009, doi: 10.2478/v10037-009-0014-x. [16] Beata Padlewska. Families of sets. Formalized Mathematics , 1( 1 ):147-152, 1990. [17] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [18] Andrzej Trybulec. On the sets

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Formalization of the Data Encryption Standard

Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics , 4( 1 ):83-86, 1993. [15] U.S. Department of Commerce/National Institute of Standards and Technology. Fips pub 46-3, data encryption standard (DES). http://csrc.nist.gov/publications/fips/-fips46-3/fips46-3.pdf. Federal Information Processing Standars Publication , 1999. [16] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [17] Michał J. Trybulec. Integers. Formalized Mathematics , 1( 3 ):501-505, 1990

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Banach Algebra of Bounded Complex-Valued Functionals

. [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics , 1( 2 ):329-334, 1990. [18] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [19] Wojciech A. Trybulec. Groups. Formalized Mathematics , 1( 5 ):821-827, 1990. [20] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics , 1( 2 ):291-296, 1990. [21] Zinaida Trybulec. Properties of subsets. Formalized

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Free Interpretation, Quotient Interpretation and Substitution of a Letter with a Term for First Order Languages

-334, 1990. Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1( 1 ):67-71, 1990. Edmund Woronowicz. Many-argument relations. Formalized Mathematics , 1( 4 ):733-737, 1990. Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics , 1( 1 ):73-83, 1990. Edmund Woronowicz. Relations defined on sets

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Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms

. On the isomorphism between finite chains. Formalized Mathematics , 9( 2 ):429-430, 2001. Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. Michał J. Trybulec. Integers. Formalized Mathematics , 1( 3 ):501-505, 1990. Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1( 1 ):67-71, 1990. Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics , 1( 1 ):73-83, 1990

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Banach Algebra of Bounded Functionals

, 11(4):377-380, 2003. [21] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1(1):115-122, 1990. [22] Wojciech A. Trybulec. Groups. Formalized Mathematics , 1(5):821-827, 1990. [23] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics , 1(2):291-296, 1990. [24] Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1(1):67-71, 1990. [25] Edmund Woronowicz. Relations

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Constructing Binary Huffman Tree
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on finite set and real-valued random variables. Formalized Mathematics , 17( 2 ):129-136, 2009. doi:10.2478/v10037-009-0014-x. [20] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ): 115-122, 1990. [21] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics , 1 ( 2 ):329-334, 1990. [22] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics , 11( 4 ): 341-347, 2003. [23] Michał J. Trybulec. Integers. Formalized

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Continuity of Bounded Linear Operators on Normed Linear Spaces

Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics , 12( 3 ):269–275, 2004. [10] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics , 19( 1 ):51–59, 2011. doi:10.2478/v10037-011-0009-2. [11] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics , 12( 1 ):39–48, 2004. [12] Yasunari Shidama. The series on Banach algebra. Formalized Mathematics , 12( 2 ):131–138, 2004. [13] Kosaku Yoshida

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Baire's Category Theorem and Some Spaces Generated from Real Normed Space1

. Real normed space. Formalized Mathematics , 2(1):111-115, 1991. [19] Bartłomiej Skorulski. First-countable, sequential, and Frechet spaces. Formalized Mathematics , 7(1):81-86, 1998. [20] Bartłomiej Skorulski. The sequential closure operator in sequential and Frechet spaces. Formalized Mathematics , 8(1):47-54, 1999. [21] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. [22] Andrzej Trybulec. Domains and their Cartesian

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Propositional Linear Temporal Logic with Initial Validity Semantics

Mathematics , 19( 2 ):113–119, 2011. doi:10.2478/v10037-011-0018-1. [11] Adam Grabowski. Hilbert positive propositional calculus. Formalized Mathematics , 8( 1 ): 69–72, 1999. [12] Fred Kröger and Stephan Merz. Temporal Logic and State Systems . Springer-Verlag, 2008. [13] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ): 115–122, 1990. [14] Andrzej Trybulec. Defining by structural induction in the positive propositional language. Formalized Mathematics , 8( 1 ):133–137, 1999. [15] Zinaida Trybulec

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