@Preamble{"\providecommand{\calR}{\cal R} \providecommand{\calE}{\cal E} \providecommand{\rmT}{\rm T} \providecommand{\BbbR}{\mathbb R} \providecommand{\SCM}{\bf SCM} \providecommand{\SCMFSA}{${\bf SCM}_{\rm FSA}$}"}
@MISC(FF_SIEC.ABS,
      AUTHOR = {Korczy\'nski, Waldemar},
      TITLE  = {Definitions of {P}etri Net -- Part {I} -- {\tt FF\_SIEC}},
      HOWPUBLISHED = {Mizar Mathematical Library},
      YEAR = {1992})

@MISC(E_SIEC.ABS,
      AUTHOR = {Korczy\'nski, Waldemar},
      TITLE  = {Definitions of {P}etri Net -- Part {II} -- {\tt E\_SIEC}},
      HOWPUBLISHED = {Mizar Mathematical Library},
      YEAR = {1992})

@MISC(S_SIEC.ABS,
      AUTHOR = {Korczy\'nski, Waldemar},
      TITLE  = {Definitions of {P}etri Net -- Part {III} -- {\tt S\_SIEC}},
      HOWPUBLISHED = {Mizar Mathematical Library},
      YEAR = {1992})

@ARTICLE(ARYTM_0.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Introduction to Arithmetics},
      JOURNAL = {To appear in Formalized Mathematics})

@ARTICLE(ARYTM_3.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Arithmetic of Non-Negative Rational Numbers},
      JOURNAL = {To appear in Formalized Mathematics})

@ARTICLE(BINOP_2.ABS,
      AUTHOR  = {Library Committee of the Association of Mizar Users},
      TITLE   = {Binary Operations on Numbers},
      JOURNAL = {To appear in Formalized Mathematics})

@ARTICLE(NUMBERS.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Subsets of Complex Numbers},
      JOURNAL = {To appear in Formalized Mathematics})

@ARTICLE(TARSKI.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Tarski {G}rothendieck Set Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {9--11})

@ARTICLE(AXIOMS.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Built-in Concepts},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {13--15})

@ARTICLE(BOOLE.ABS,
      AUTHOR  = {Trybulec, Zinaida and {\'{S}}wi\k{e}czkowska, Halina},
      TITLE   = {Boolean Properties of Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {17--23})

@ARTICLE(ENUMSET1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Enumerated Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {25--34})

@ARTICLE(REAL_1.ABS,
      AUTHOR  = {Hryniewiecki, Krzysztof},
      TITLE   = {Basic Properties  of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {35--40})

@ARTICLE(NAT_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {The Fundamental Properties of Natural Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {41--46})

@ARTICLE(ZFMISC_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Some Basic Properties of Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {47--53})

@ARTICLE(FUNCT_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Functions and Their Basic Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {55--65})

@ARTICLE(SUBSET_1.ABS,
      AUTHOR  = {Trybulec, Zinaida},
      TITLE   = {Properties of Subsets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {67--71})

@ARTICLE(RELAT_1.ABS,
      AUTHOR  = {Woronowicz, Edmund},
      TITLE   = {Relations and Their Basic Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {73--83})

@ARTICLE(RELAT_2.ABS,
      AUTHOR  = {Woronowicz, Edmund and Zalewska, Anna},
      TITLE   = {Properties of Binary Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {85--89})

@ARTICLE(ORDINAL1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {The Ordinal Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {91--96})

@ARTICLE(MCART_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Tuples, Projections and {C}artesian Products},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {97--105})

@ARTICLE(FINSEQ_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Hryniewiecki, Krzysztof},
      TITLE   = {Segments of Natural Numbers and Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {107--114})

@ARTICLE(DOMAIN_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Domains and Their {C}artesian Products},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {115--122})

@ARTICLE(WELLORD1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {The Well Ordering Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {123--129})

@ARTICLE(ZF_LANG.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {A Model of {ZF} Set Theory Language},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {131--145})

@ARTICLE(SETFAM_1.ABS,
      AUTHOR  = {Padlewska, Beata},
      TITLE   = {Families of Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {147--152})

@ARTICLE(FUNCT_2.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Functions from a Set to a Set},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {153--164})

@ARTICLE(FINSET_1.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata},
      TITLE   = {Finite Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {165--167})

@ARTICLE(GRFUNC_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Graphs of Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {169--173})

@ARTICLE(BINOP_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Binary Operations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {175--180})

@ARTICLE(RELSET_1.ABS,
      AUTHOR  = {Woronowicz, Edmund},
      TITLE   = {Relations Defined on Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {181--186})

@ARTICLE(FINSUB_1.ABS,
      AUTHOR  = {Trybulec, Andrzej and Darmochwa{\l}, Agata},
      TITLE   = {Boolean Domains},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {187--190})

@ARTICLE(ZF_MODEL.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Models and Satisfiability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {191--199})

@ARTICLE(ZF_COLLA.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {The Contraction Lemma},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {201--203})

@ARTICLE(INCSP_1.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Axioms of Incidence},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {205--213})

@ARTICLE(LATTICES.ABS,
      AUTHOR  = {{\.{Z}}ukowski, Stanis{\l}aw},
      TITLE   = {Introduction to Lattice Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {215--222})

@ARTICLE(PRE_TOPC.ABS,
      AUTHOR  = {Padlewska, Beata and Darmochwa{\l}, Agata},
      TITLE   = {Topological Spaces and Continuous Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {223--230})

@ARTICLE(TOPS_1.ABS,
      AUTHOR  = {Wysocki, Miros{\l}aw and Darmochwa{\l}, Agata},
      TITLE   = {Subsets of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {231--237})

@ARTICLE(CONNSP_1.ABS,
      AUTHOR  = {Padlewska, Beata},
      TITLE   = {Connected Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {239--244})

@ARTICLE(FUNCT_3.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Basic Functions and Operations on Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      NUMBER  = {{\bf 1}},
      VOLUME  = 1,
      PAGES   = {245--254})

@ARTICLE(TOPS_2.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata},
      TITLE   = {Families of Subsets, Subspaces and Mappings in Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {257--261},
      NUMBER  = {{\bf 2}})

@ARTICLE(ANAL_1.ABS,
      AUTHOR  = {Popio{\l}ek, Jan},
      TITLE   = {Some Properties of Functions Modul and Signum},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {263--264},
      NUMBER  = {{\bf 2}})

@ARTICLE(ABSVALUE.ABS,
      AUTHOR  = {Popio{\l}ek, Jan},
      TITLE   = {Some Properties of Functions Modul and Signum},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {263--264},
      NUMBER  = {{\bf 2}})

@ARTICLE(WELLORD2.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Zermelo Theorem and Axiom of Choice},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {265--267},
      NUMBER  = {{\bf 2}})

@ARTICLE(SEQ_1.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Real Sequences and Basic Operations on Them},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {269--272},
      NUMBER  = {{\bf 2}})

@ARTICLE(SEQ_2.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Convergent Sequences and the Limit of Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {273--275},
      NUMBER  = {{\bf 2}})

@ARTICLE(ZFMODEL1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Properties of {ZF} Models},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {277--280},
      NUMBER  = {{\bf 2}})

@ARTICLE(ORDINAL2.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Sequences of Ordinal Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {281--290},
      NUMBER  = {{\bf 2}})

@ARTICLE(RLVECT_1.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Vectors in Real Linear Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {291--296},
      NUMBER  = {{\bf 2}})

@ARTICLE(RLSUB_1.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Subspaces and Cosets of Subspaces in Real Linear Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {297--301},
      NUMBER  = {{\bf 2}})

@ARTICLE(QC_LANG1.ABS,
      AUTHOR  = {Rudnicki, Piotr and Trybulec, Andrzej},
      TITLE   = {A First Order Language},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {303--311},
      NUMBER  = {{\bf 2}})

@ARTICLE(ORDERS_1.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Partially Ordered Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {313--319},
      NUMBER  = {{\bf 2}})

@ARTICLE(RECDEF_1.ABS,
      AUTHOR  = {Hryniewiecki, Krzysztof},
      TITLE   = {Recursive Definitions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {321--328},
      NUMBER  = {{\bf 2}})

@ARTICLE(FUNCOP_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Binary Operations Applied to Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {329--334},
      NUMBER  = {{\bf 2}})

@ARTICLE(VECTSP_1.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Leo{\'n}czuk, Wojciech and Muzalewski, Micha{\l}},
      TITLE   = {Abelian Groups, Fields and Vector Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {335--342},
      NUMBER  = {{\bf 2}})

@ARTICLE(PARSP_1.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Leo{\'n}czuk, Wojciech and Muzalewski, Micha{\l}},
      TITLE   = {Parallelity Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {343--348},
      NUMBER  = {{\bf 2}})

@ARTICLE(SYMSP_1.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Leo{\'n}czuk, Wojciech and Muzalewski, Micha{\l}},
      TITLE   = {Construction of a bilinear antisymmetric form in simplectic vector space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {349--352},
      NUMBER  = {{\bf 2}})

@ARTICLE(ORTSP_1.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Leo{\'n}czuk, Wojciech and Muzalewski, Micha{\l}},
      TITLE   = {Construction of a bilinear symmetric form in orthogonal vector space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {353--356},
      NUMBER  = {{\bf 2}})

@ARTICLE(PARTFUN1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Partial Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {357--367},
      NUMBER  = {{\bf 2}})

@ARTICLE(SETWISEO.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Semilattice Operations on Finite Subsets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {369--376},
      NUMBER  = {{\bf 2}})

@ARTICLE(CARD_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Cardinal Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {377--382},
      NUMBER  = {{\bf 2}})

@ARTICLE(COMPTS_1.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata},
      TITLE   = {Compact Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {383--386},
      NUMBER  = {{\bf 2}})

@ARTICLE(ORDERS_2.ABS,
      AUTHOR  = {Trybulec, Wojciech A. and Bancerek, Grzegorz},
      TITLE   = {Kuratowski -- {Z}orn Lemma},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {387--393},
      NUMBER  = {{\bf 2}})

@ARTICLE(RLSUB_2.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Operations on Subspaces in Real Linear Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {395--399},
      NUMBER  = {{\bf 2}})

@ARTICLE(PROB_1.ABS,
      AUTHOR  = {N\k{e}dzusiak, Andrzej},
      TITLE   = { $\sigma$-Fields and Probability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {401--407},
      NUMBER  = {{\bf 2}})

@ARTICLE(CAT_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Introduction to Categories and Functors},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {409--420},
      NUMBER  = {{\bf 2}})

@ARTICLE(TREES_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Introduction to Trees},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {421--427},
      NUMBER  = {{\bf 2}})

@ARTICLE(WELLSET1.ABS,
      AUTHOR  = {Nowak, Bogdan and Bia{\l}ecki, S{\l}awomir},
      TITLE   = {Zermelo's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {431--432},
      NUMBER  = {{\bf 3}})

@ARTICLE(REALSET1.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {Group and Field Definitions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {433--439},
      NUMBER  = {{\bf 3}})

@ARTICLE(EQREL_1.ABS,
      AUTHOR  = {Raczkowski, Konrad and Sadowski, Pawe{\l}},
      TITLE   = {Equivalence Relations and Classes of Abstraction},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {441--444},
      NUMBER  = {{\bf 3}})

@ARTICLE(SQUARE_1.ABS,
      AUTHOR  = {Trybulec, Andrzej and Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Some Properties of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {445--449},
      NUMBER  = {{\bf 3}})

@ARTICLE(QC_LANG2.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Connectives and Subformulae of the First Order Language},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {451--458},
      NUMBER  = {{\bf 3}})

@ARTICLE(QC_LANG3.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw and Bancerek, Grzegorz},
      TITLE   = {Variables in Formulae of the First Order Language},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {459--469},
      NUMBER  = {{\bf 3}})

@ARTICLE(SEQM_3.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Monotone Real Sequences. {S}ubsequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {471--475},
      NUMBER  = {{\bf 3}})

@ARTICLE(SEQ_4.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Convergent Real Sequences. {U}pper and Lower Bound of Sets of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {477--481},
      NUMBER  = {{\bf 3}})

@ARTICLE(MIDSP_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Midpoint algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {483--488},
      NUMBER  = {{\bf 3}})

@ARTICLE(QMAX_1.ABS,
      AUTHOR  = {Sadowski, Pawe{\l} and Trybulec, Andrzej and Raczkowski, Konrad},
      TITLE   = {The Fundamental Logic Structure in Quantum Mechanics},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {489--494},
      NUMBER  = {{\bf 3}})

@ARTICLE(FRAENKEL.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Function Domains and {F}r{\ae}nkel Operator},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {495--500},
      NUMBER  = {{\bf 3}})

@ARTICLE(INT_1.ABS,
      AUTHOR  = {Trybulec, Micha{\l} J.},
      TITLE   = {Integers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {501--505},
      NUMBER  = {{\bf 3}})

@ARTICLE(COMPLEX1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {The Complex Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {507--513},
      NUMBER  = {{\bf 3}})

@ARTICLE(ORDINAL3.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Ordinal Arithmetics},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {515--519},
      NUMBER  = {{\bf 3}})

@ARTICLE(FUNCT_4.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {The Modification of a Function by a Function and the Iteration of the Composition of a Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {521--527},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINSEQ_2.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Finite Sequences and Tuples of Elements of a Non-empty Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {529--536},
      NUMBER  = {{\bf 3}})

@ARTICLE(FUNCT_5.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Curried and Uncurried Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {537--541},
      NUMBER  = {{\bf 3}})

@ARTICLE(CARD_2.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Cardinal Arithmetics},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {543--547},
      NUMBER  = {{\bf 3}})

@ARTICLE(PARSP_2.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Leo{\'n}czuk, Wojciech},
      TITLE   = {Fano-{D}esargues Parallelity Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {549--553},
      NUMBER  = {{\bf 3}})

@ARTICLE(FUNCSDOM.ABS,
      AUTHOR  = {Oryszczyszyn , Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Real Functions Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {555--561},
      NUMBER  = {{\bf 3}})

@ARTICLE(CLASSES1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Tarski's Classes and Ranks},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {563--567},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINSEQ_3.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Non-contiguous Substrings and One-to-one Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {569--573},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINSEQ_4.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Pigeon Hole Principle},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {575--579},
      NUMBER  = {{\bf 3}})

@ARTICLE(RLVECT_2.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Linear Combinations in Real Linear Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {581--588},
      NUMBER  = {{\bf 3}})

@ARTICLE(CARD_3.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {K{\"o}nig's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {589--593},
      NUMBER  = {{\bf 3}})

@ARTICLE(CLASSES2.ABS,
      AUTHOR  = {Nowak, Bogdan and Bancerek, Grzegorz},
      TITLE   = {Universal Classes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {595--600},
      NUMBER  = {{\bf 3}})

@ARTICLE(ANALOAF.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Analytical Ordered Affine Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {601--605},
      NUMBER  = {{\bf 3}})

@ARTICLE(METRIC_1.ABS,
      AUTHOR  = {Kanas, Stanis{\l}awa and Lecko, Adam and Startek, Mariusz},
      TITLE   = {Metric Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {607--610},
      NUMBER  = {{\bf 3}})

@ARTICLE(DIRAF.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Ordered Affine Spaces Defined in Terms of Directed Parallelity -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {611--615},
      NUMBER  = {{\bf 3}})

@ARTICLE(AFF_1.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Parallelity and Lines in Affine Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {617--621},
      NUMBER  = {{\bf 3}})

@ARTICLE(AFF_2.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Classical Configurations in Affine Planes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {625--633},
      NUMBER  = {{\bf 4}})

@ARTICLE(AFF_3.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Affine Localizations of {D}esargues Axiom},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {635--642},
      NUMBER  = {{\bf 4}})

@ARTICLE(FINSEQOP.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Binary Operations Applied to Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {643--649},
      NUMBER  = {{\bf 4}})

@ARTICLE(SETWOP_2.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Semigroup operations on finite subsets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {651--656},
      NUMBER  = {{\bf 4}})

@ARTICLE(COLLSP.ABS,
      AUTHOR  = {Skaba, Wojciech},
      TITLE   = {The Collinearity Structure},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {657--659},
      NUMBER  = {{\bf 4}})

@ARTICLE(RVSUM_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {The Sum and Product of Finite Sequences of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {661--668},
      NUMBER  = {{\bf 4}})

@ARTICLE(CQC_LANG.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {A Classical First Order Language},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {669--676},
      NUMBER  = {{\bf 4}})

@ARTICLE(PASCH.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof and Pra{\.z}mowska, Ma{\l}gorzata},
      TITLE   = {Classical and Non--classical {P}asch Configurations in Ordered Affine Planes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {677--680},
      NUMBER  = {{\bf 4}})
      
@ARTICLE(REAL_LAT.ABS,
      AUTHOR  = {Chmur, Marek},
      TITLE   = {The Lattice of Real Numbers. {T}he Lattice of Real Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {681--684},
      NUMBER  = {{\bf 4}})

@ARTICLE(TDGROUP.ABS,
      AUTHOR  = {Lewandowski, Grzegorz and Pra{\.z}mowski, Krzysztof},
      TITLE   = {A Construction of an Abstract Space of Congruence of Vectors},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {685--688},
      NUMBER  = {{\bf 4}})

@ARTICLE(CQC_THE1.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata},
      TITLE   = {A First--Order Predicate Calculus},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {689--695},
      NUMBER  = {{\bf 4}})

@ARTICLE(PARTFUN2.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Partial Functions from a Domain to a Domain},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {697--702},
      NUMBER  = {{\bf 4}})

@ARTICLE(RFUNCT_1.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Partial Functions from a Domain to the Set of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {703--709},
      NUMBER  = {{\bf 4}})

@ARTICLE(ORDINAL4.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Increasing and Continuous Ordinal Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {711--714},
      NUMBER  = {{\bf 4}})

@ARTICLE(TRANSGEO.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Transformations in Affine Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {715--723},
      NUMBER  = {{\bf 4}})

@ARTICLE(CAT_2.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Subcategories and Products of Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {725--732},
      NUMBER  = {{\bf 4}})

@ARTICLE(MARGREL1.ABS,
      AUTHOR  = {Woronowicz, Edmund},
      TITLE   = {Many--Argument Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {733--737},
      NUMBER  = {{\bf 4}})

@ARTICLE(VALUAT_1.ABS,
      AUTHOR  = {Woronowicz, Edmund},
      TITLE   = {Interpretation and Satisfiability in the First Order Logic},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {739--743},
      NUMBER  = {{\bf 4}})

@ARTICLE(PROB_2.ABS,
      AUTHOR  = {N\k{e}dzusiak, Andrzej},
      TITLE   = {Probability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {745--749},
      NUMBER  = {{\bf 4}})

@ARTICLE(TRANSLAC.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Translations in Affine Planes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {751--753},
      NUMBER  = {{\bf 4}})

@ARTICLE(RPR_1.ABS,
      AUTHOR  = {Popio{\l}ek, Jan},
      TITLE   = {Introduction to Probability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {755--760},
      NUMBER  = {{\bf 4}})

@ARTICLE(ANPROJ_1.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {A Construction of Analytical Projective Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {761--766},
      NUMBER  = {{\bf 4}})

@ARTICLE(ANPROJ_2.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Projective Spaces -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {767--776},
      NUMBER  = {{\bf 4}})

@ARTICLE(RCOMP_1.ABS,
      AUTHOR  = {Raczkowski, Konrad and Sadowski, Pawe{\l}},
      TITLE   = {Topological Properties of Subsets in Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {777--780},
      NUMBER  = {{\bf 4}})

@ARTICLE(RFUNCT_2.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Properties of Real Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {781--786},
      NUMBER  = {{\bf 4}})

@ARTICLE(FCONT_1.ABS,
      AUTHOR  = {Raczkowski, Konrad and Sadowski, Pawe{\l}},
      TITLE   = {Real Function Continuity},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {787--791},
      NUMBER  = {{\bf 4}})

@ARTICLE(FCONT_2.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Raczkowski, Konrad},
      TITLE   = {Real Function Uniform Continuity},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {793--795},
      NUMBER  = {{\bf 4}})

@ARTICLE(FDIFF_1.ABS,
      AUTHOR  = {Raczkowski, Konrad and Sadowski, Pawe{\l}},
      TITLE   = {Real Function Differentiability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {797--801},
      NUMBER  = {{\bf 4}})

@ARTICLE(ROLLE.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Raczkowski, Konrad and Sadowski, Pawe{\l}},
      TITLE   = {Average Value Theorems for Real Functions of One Variable},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {803--805},
      NUMBER  = {{\bf 4}})

@ARTICLE(REALSET2.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {Properties of Fields},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {807--812},
      NUMBER  = {{\bf 5}})

@ARTICLE(FILTER_0.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Filters -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {813--819},
      NUMBER  = {{\bf 5}})

@ARTICLE(GROUP_1.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {821--827},
      NUMBER  = {{\bf 5}})

@ARTICLE(INT_2.ABS,
      AUTHOR  = {Kwiatek, Rafa{\l} and Zwara, Grzegorz},
      TITLE   = {The Divisibility of Integers and Integer Relative Primes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {829--832},
      NUMBER  = {{\bf 5}})

@ARTICLE(ALGSTR_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {From Loops to Abelian Multiplicative Groups with Zero},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {833--840},
      NUMBER  = {{\bf 5}})

@ARTICLE(RAT_1.ABS,
      AUTHOR  = {Kondracki, Andrzej},
      TITLE   = {Basic Properties of Rational Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {841--845},
      NUMBER  = {{\bf 5}})

@ARTICLE(RLVECT_3.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Basis of Real Linear Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {847--850},
      NUMBER  = {{\bf 5}})

@ARTICLE(VECTSP_3.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Finite Sums of Vectors in Vector Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {851--854},
      NUMBER  = {{\bf 5}})

@ARTICLE(GROUP_2.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Subgroup and Cosets of Subgroups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {855--864},
      NUMBER  = {{\bf 5}})

@ARTICLE(VECTSP_4.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Subspaces and Cosets of Subspaces in Vector Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {865--870},
      NUMBER  = {{\bf 5}})

@ARTICLE(VECTSP_5.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Operations on Subspaces in Vector Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {871--876},
      NUMBER  = {{\bf 5}})

@ARTICLE(VECTSP_6.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Linear Combinations in Vector Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {877--882},
      NUMBER  = {{\bf 5}})

@ARTICLE(VECTSP_7.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Basis of Vector Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {883--885},
      NUMBER  = {{\bf 5}})

@ARTICLE(NEWTON.ABS,
      AUTHOR  = {Kwiatek, Rafa{\l}},
      TITLE   = {Factorial and {N}ewton coefficients},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {887--890},
      NUMBER  = {{\bf 5}})

@ARTICLE(ANALMETR.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Analytical Metric Affine Spaces and Planes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {891--899},
      NUMBER  = {{\bf 5}})

@ARTICLE(ANPROJ_3.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Projective Spaces -- part {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {901--907},
      NUMBER  = {{\bf 5}})

@ARTICLE(ANPROJ_4.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Projective Spaces -- part {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {909--918},
      NUMBER  = {{\bf 5}})

@ARTICLE(ANPROJ_5.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Projective Spaces -- part {IV}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {919--927},
      NUMBER  = {{\bf 5}})

@ARTICLE(ANPROJ_6.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Projective Spaces -- part {V}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {929--938},
      NUMBER  = {{\bf 5}})

@ARTICLE(ANPROJ_7.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Projective Spaces -- part {VI}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {939--947},
      NUMBER  = {{\bf 5}})

@ARTICLE(NET_1.ABS,
      AUTHOR  = {Korczy{\'n}ski, Waldemar},
      TITLE   = {Some Elementary Notions of the Theory of {P}etri Nets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {949--953},
      NUMBER  = {{\bf 5}})

@ARTICLE(GROUP_3.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Classes of Conjugation. {N}ormal Subgroups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {955--962},
      NUMBER  = {{\bf 5}})

@ARTICLE(ZF_LANG1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Replacing of Variables in Formulas of {ZF} Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {963--972},
      NUMBER  = {{\bf 5}})

@ARTICLE(ZF_REFLE.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {The Reflection Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {973--977},
      NUMBER  = {{\bf 5}})

@ARTICLE(FINSOP_1.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Binary Operations on Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {979--981},
      NUMBER  = {{\bf 5}})

@ARTICLE(LATTICE2.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Finite Join and Finite Meet and Dual Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {983--988},
      NUMBER  = {{\bf 5}})

@ARTICLE(ZFREFLE1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Consequences of the Reflection Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1990},
      VOLUME  = 1,
      PAGES   = {989--993},
      NUMBER  = {{\bf 5}})

@ARTICLE(VECTSP_2.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Construction of Rings and Left-, Right-, and Bi-Modules over a Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {3--11},
      NUMBER  = {{\bf 1}})

@ARTICLE(PROJDES1.ABS,
      AUTHOR  = {Kusak, Eugeniusz},
      TITLE   = {Desargues Theorem In Projective 3-Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {13--16},
      NUMBER  = {{\bf 1}})

@ARTICLE(LIMFUNC1.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {The Limit of a Real Function at Infinity},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {17--28},
      NUMBER  = {{\bf 1}})

@ARTICLE(LIMFUNC2.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {One-Side Limits of a Real Function at a Point},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {29--40},
      NUMBER  = {{\bf 1}})

@ARTICLE(GROUP_4.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Lattice of Subgroups of a Group. {F}rattini Subgroup},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {41--47},
      NUMBER  = {{\bf 1}})

@ARTICLE(REAL_2.ABS,
      AUTHOR  = {Kondracki, Andrzej},
      TITLE   = {Equalities and Inequalities in Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {49--63},
      NUMBER  = {{\bf 1}})

@ARTICLE(CARD_4.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Countable Sets and {H}essenberg's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {65--69},
      NUMBER  = {{\bf 1}})

@ARTICLE(LIMFUNC3.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {The Limit of a Real Function at a Point},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {71--80},
      NUMBER  = {{\bf 1}})

@ARTICLE(LIMFUNC4.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {The Limit of a Composition of Real Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {81--92},
      NUMBER  = {{\bf 1}})

@ARTICLE(CONNSP_2.ABS,
      AUTHOR  = {Padlewska, Beata},
      TITLE   = {Locally Connected Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {93--96},
      NUMBER  = {{\bf 1}})

@ARTICLE(ALGSEQ_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Szczerba, Les{\l}aw W.},
      TITLE   = {Construction of Finite Sequences over Ring and Left-, Right-,  and Bi-Modules over a Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {97--104},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOLER_1.ABS,
      AUTHOR  = {Hryniewiecki, Krzysztof},
      TITLE   = {Relations of Tolerance},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {105--109},
      NUMBER  = {{\bf 1}})

@ARTICLE(NORMSP_1.ABS,
      AUTHOR  = {Popio{\l}ek, Jan},
      TITLE   = {Real Normed Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {111--115},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCHEME1.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Schemes of Existence of some Types of Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {117--123},
      NUMBER  = {{\bf 1}})

@ARTICLE(PREPOWER.ABS,
      AUTHOR  = {Raczkowski, Konrad},
      TITLE   = {Integer and Rational Exponents},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {125--130},
      NUMBER  = {{\bf 1}})

@ARTICLE(HOMOTHET.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Homotheties and Shears in Affine Planes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {131--133},
      NUMBER  = {{\bf 1}})

@ARTICLE(AFVECT0.ABS,
      AUTHOR  = {Lewandowski, Grzegorz and Pra{\.z}mowski, Krzysztof and Lewandowska, Bo{\.z}ena},
      TITLE   = {Directed Geometrical Bundles and Their Analytical Representation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {135--141},
      NUMBER  = {{\bf 1}})

@ARTICLE(ZFMODEL2.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Definable Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {143--145},
      NUMBER  = {{\bf 1}})

@ARTICLE(LUKASI_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz  and Darmochwa{\l}, Agata and Trybulec, Andrzej},
      TITLE   = {Propositional Calculus},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {147--150},
      NUMBER  = {{\bf 1}})

@ARTICLE(COMPLSP1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw and Trybulec, Andrzej},
      TITLE   = {Complex Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {151--158},
      NUMBER  = {{\bf 1}})

@ARTICLE(REALSET3.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {Several Properties of Fields. {F}ield Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {159--162},
      NUMBER  = {{\bf 1}})

@ARTICLE(SUPINF_1.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {Infimum and Supremum of the Set of Real Numbers. {M}easure Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {163--171},
      NUMBER  = {{\bf 1}})

@ARTICLE(SUPINF_2.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {Series of  Positive Real Numbers. {M}easure Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {173--183},
      NUMBER  = {{\bf 1}})

@ARTICLE(ALGSTR_2.ABS,
      AUTHOR  = {Skaba, Wojciech and Muzalewski, Micha{\l}},
      TITLE   = {From Double Loops to Fields},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {185--191},
      NUMBER  = {{\bf 1}})

@ARTICLE(METRIC_3.ABS,
      AUTHOR  = {Kanas, Stanis{\l}awa and Stankiewicz, Jan},
      TITLE   = {Metrics in {C}artesian Product},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {193--197},
      NUMBER  = {{\bf 2}})

@ARTICLE(SUB_METR.ABS,
      AUTHOR  = {Lecko, Adam and Startek, Mariusz},
      TITLE   = {Submetric Spaces -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {199--203},
      NUMBER  = {{\bf 2}})

@ARTICLE(METRIC_2.ABS,
      AUTHOR  = {Lecko, Adam and Startek, Mariusz},
      TITLE   = {On Pseudometric Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {205--211},
      NUMBER  = {{\bf 2}})

@ARTICLE(POWER.ABS,
      AUTHOR  = {Raczkowski, Konrad and N\k{e}dzusiak, Andrzej},
      TITLE   = {Real Exponents and Logarithms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {213--216},
      NUMBER  = {{\bf 2}})

@ARTICLE(HESSENBE.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Leo{\'n}czuk, Wojciech},
      TITLE   = {Hessenberg Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {217--219},
      NUMBER  = {{\bf 2}})

@ARTICLE(MULTOP_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {Three-Argument Operations and Four-Argument Operations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {221--224},
      NUMBER  = {{\bf 2}})

@ARTICLE(INCPROJ.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Incidence Projective Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {225--232},
      NUMBER  = {{\bf 2}})

@ARTICLE(AFVECT01.ABS,
      AUTHOR  = {Konstanta, Barbara and Kowieska, Urszula and Lewandowski, Grzegorz and Pra{\.z}mowski, Krzysztof},
      TITLE   = {One-Dimensional Congruence of Segments, Basic Facts and Midpoint  Relation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {233--235},
      NUMBER  = {{\bf 2}})

@ARTICLE(NORMFORM.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Algebra of Normal Forms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {237--242},
      NUMBER  = {{\bf 2}})

@ARTICLE(O_RING_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Szczerba, Les{\l}aw W.},
      TITLE   = {Ordered Rings -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {243--245},
      NUMBER  = {{\bf 2}})

@ARTICLE(O_RING_2.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Szczerba, Les{\l}aw W.},
      TITLE   = {Ordered Rings -- Part {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {247--249},
      NUMBER  = {{\bf 2}})

@ARTICLE(O_RING_3.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Szczerba, Les{\l}aw W.},
      TITLE   = {Ordered Rings -- Part {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {251--253},
      NUMBER  = {{\bf 2}})

@ARTICLE(MCART_2.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {{N}-Tuples and {C}artesian Products for n$=$5},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {255--258},
      NUMBER  = {{\bf 2}})

@ARTICLE(ALGSTR_3.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {Ternary Fields},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {259--261},
      NUMBER  = {{\bf 2}})

@ARTICLE(MEASURE1.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {The $\sigma$-additive Measure Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {263--270},
      NUMBER  = {{\bf 2}})

@ARTICLE(PROJRED1.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Leo{\'n}czuk, Wojciech},
      TITLE   = {Incidence Projective Space (a reduction theorem in a plane)},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {271--274},
      NUMBER  = {{\bf 2}})

@ARTICLE(MOD_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {Groups, Rings, Left- and Right-Modules},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {275--278},
      NUMBER  = {{\bf 2}})

@ARTICLE(LMOD_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {Finite Sums of Vectors in Left Module over Associative Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {279--282},
      NUMBER  = {{\bf 2}})

@ARTICLE(LMOD_2.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {Submodules and Cosets of Submodules in Left Module over Associative Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {283--287},
      NUMBER  = {{\bf 2}})

@ARTICLE(LMOD_3.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {Operations on Submodules in Left Module over Associative Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {289--293},
      NUMBER  = {{\bf 2}})

@ARTICLE(LMOD_4.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {Linear Combinations in Left Module over Associative Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {295--300},
      NUMBER  = {{\bf 2}})

@ARTICLE(LMOD_5.ABS,
      AUTHOR  = {Muzalewski, Micha{\l} and Skaba, Wojciech},
      TITLE   = {Linear Independence in Left Module over Domain},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {301--303},
      NUMBER  = {{\bf 2}})

@ARTICLE(PROCAL_1.ABS,
      AUTHOR  = {Popio{\l}ek, Jan and Trybulec, Andrzej},
      TITLE   = {Calculus of Propositions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {305--307},
      NUMBER  = {{\bf 2}})

@ARTICLE(CQC_THE2.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata},
      TITLE   = {Calculus of Quantifiers. {D}eduction Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {309--312},
      NUMBER  = {{\bf 2}})

@ARTICLE(ANALTRAP.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {A construction of analytical Ordered Trapezium Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {315--322},
      NUMBER  = {{\bf 3}})

@ARTICLE(GEOMTRAP.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {A construction of analytical Ordered Trapezium Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {315--322},
      NUMBER  = {{\bf 3}})

@ARTICLE(PROJRED2.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Leo{\'n}czuk, Wojciech and Pra{\.z}mowski, Krzysztof},
      TITLE   = {On Projections in Projective Planes ({P}art {II} )},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {323--329},
      NUMBER  = {{\bf 3}})

@ARTICLE(CONAFFM.ABS,
      AUTHOR  = {{\'{S}}wierzy{\'n}ska, Jolanta and {\'{S}}wierzy{\'n}ski, Bogdan},
      TITLE   = {Metric-Affine Configurations in Metric Affine Planes -- {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {331--334},
      NUMBER  = {{\bf 3}})

@ARTICLE(CONMETR.ABS,
      AUTHOR  = {{\'{S}}wierzy{\'n}ska, Jolanta and {\'{S}}wierzy{\'n}ski, Bogdan},
      TITLE   = {Metric-Affine Configurations in Metric Affine Planes -- {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {335--340},
      NUMBER  = {{\bf 3}})

@ARTICLE(PAPDESAF.ABS,
      AUTHOR  = {Pra{\.z}mowski, Krzysztof},
      TITLE   = {{F}anoian, {P}appian and {D}esarguesian Affine Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {341--346},
      NUMBER  = {{\bf 3}})

@ARTICLE(PARDEPAP.ABS,
      AUTHOR  = {Pra{\.z}mowski, Krzysztof and Radziszewski, Krzysztof},
      TITLE   = {Elementary Variants of Affine Configurational Theorems},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {347--348},
      NUMBER  = {{\bf 3}})

@ARTICLE(SEMI_AF1.ABS,
      AUTHOR  = {Kusak, Eugeniusz and Radziszewski, Krzysztof},
      TITLE   = {Semi\_Affine Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {349--356},
      NUMBER  = {{\bf 3}})

@ARTICLE(AFF_4.ABS,
      AUTHOR  = {Leo{\'n}czuk, Wojciech and Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Planes in Affine Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {357--363},
      NUMBER  = {{\bf 3}})

@ARTICLE(GRAPH_1.ABS,
      AUTHOR  = {Hryniewiecki, Krzysztof},
      TITLE   = {Graphs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {365--370},
      NUMBER  = {{\bf 3}})

@ARTICLE(ZF_FUND1.ABS,
      AUTHOR  = {Kondracki, Andrzej},
      TITLE   = {{M}ostowski's Fundamental Operations -- {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {371--375},
      NUMBER  = {{\bf 3}})

@ARTICLE(AFPROJ.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {A Projective Closure and Projective Horizon of an Affine Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {377--384},
      NUMBER  = {{\bf 3}})

@ARTICLE(SCHEMS_1.ABS,
      AUTHOR  = {Czuba, Stanis{\l}aw T.},
      TITLE   = {Schemes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {385--391},
      NUMBER  = {{\bf 3}})

@ARTICLE(HEYTING1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Algebra of Normal Forms Is a {H}eyting Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {393--396},
      NUMBER  = {{\bf 3}})

@ARTICLE(TREES_2.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {K{\"o}nig's Lemma},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {397--402},
      NUMBER  = {{\bf 3}})

@ARTICLE(FCONT_3.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Monotonic and Continuous Real Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {403--405},
      NUMBER  = {{\bf 3}})

@ARTICLE(FDIFF_2.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Raczkowski, Konrad},
      TITLE   = {Real Function Differentiability -- {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {407--411},
      NUMBER  = {{\bf 3}})

@ARTICLE(PRELAMB.ABS,
      AUTHOR  = {Zielonka, Wojciech},
      TITLE   = {Preliminaries to the {L}ambek calculus},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {413--418},
      NUMBER  = {{\bf 3}})

@ARTICLE(OPPCAT_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Opposite Categories and Contravariant Functors},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {419--424},
      NUMBER  = {{\bf 3}})

@ARTICLE(ZF_FUND2.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Kondracki, Andrzej},
      TITLE   = {{M}ostowski's Fundamental Operations -- {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {425--427},
      NUMBER  = {{\bf 3}})

@ARTICLE(EUCLMETR.ABS,
      AUTHOR  = {Oryszczyszyn, Henryk and Pra{\.z}mowski, Krzysztof},
      TITLE   = {Fundamental Types of Metric Affine Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {429--432},
      NUMBER  = {{\bf 3}})

@ARTICLE(FILTER_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Filters -- Part {II}. {Q}uotient Lattices Modulo Filters and Direct Product of Two Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {433--438},
      NUMBER  = {{\bf 3}})

@ARTICLE(CONMETR1.ABS,
      AUTHOR  = {{\'{S}}wierzy{\'n}ska, Jolanta and {\'{S}}wierzy{\'n}ski, Bogdan},
      TITLE   = {Shear Theorems and their role in Affine Geometry},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {439--444},
      NUMBER  = {{\bf 3}})

@ARTICLE(SERIES_1.ABS,
      AUTHOR  = {Raczkowski, Konrad and N\k{e}dzusiak, Andrzej},
      TITLE   = {Series},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {449--452},
      NUMBER  = {{\bf 4}})

@ARTICLE(NAT_LAT.ABS,
      AUTHOR  = {Chmur, Marek},
      TITLE   = {The Lattice of Natural Numbers and The Sublattice of it. {T}he Set of Prime Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {453--459},
      NUMBER  = {{\bf 4}})

@ARTICLE(GROUP_5.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Commutator and Center of a Group},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {461--466},
      NUMBER  = {{\bf 4}})

@ARTICLE(NATTRA_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Natural Transformations. {D}iscrete Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {467--474},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIX_1.ABS,
      AUTHOR  = {Jankowska, Katarzyna},
      TITLE   = {Matrices. {A}belian Group of Matrices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {475--480},
      NUMBER  = {{\bf 4}})

@ARTICLE(PCOMPS_1.ABS,
      AUTHOR  = {Borys, Leszek},
      TITLE   = {Paracompact and Metrizable Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {481--485},
      NUMBER  = {{\bf 4}})

@ARTICLE(MIDSP_2.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Atlas of {M}idpoint {A}lgebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {487--491},
      NUMBER  = {{\bf 4}})

@ARTICLE(MEASURE2.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {Several Properties of the $\sigma$-additive Measure},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {493--497},
      NUMBER  = {{\bf 4}})

@ARTICLE(METRIC_4.ABS,
      AUTHOR  = {Kanas, Stanis{\l}awa and Lecko, Adam},
      TITLE   = {Metrics in the {C}artesian Product -- Part {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {499--504},
      NUMBER  = {{\bf 4}})

@ARTICLE(ALI2.ABS,
      AUTHOR  = {de la Cruz, Alicia},
      TITLE   = {Fix Point Theorem for Compact Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {505--506},
      NUMBER  = {{\bf 4}})

@ARTICLE(QUIN_1.ABS,
      AUTHOR  = {Popio{\l}ek, Jan},
      TITLE   = {Quadratic Inequalities},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {507--509},
      NUMBER  = {{\bf 4}})

@ARTICLE(BHSP_1.ABS,
      AUTHOR  = {Popio{\l}ek, Jan},
      TITLE   = {Introduction to {B}anach and {H}ilbert Spaces -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {511--516},
      NUMBER  = {{\bf 4}})

@ARTICLE(BHSP_2.ABS,
      AUTHOR  = {Popio{\l}ek, Jan},
      TITLE   = {Introduction to {B}anach and {H}ilbert Spaces -- Part {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {517--521},
      NUMBER  = {{\bf 4}})

@ARTICLE(BHSP_3.ABS,
      AUTHOR  = {Popio{\l}ek, Jan},
      TITLE   = {Introduction to {B}anach and {H}ilbert Spaces -- Part {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {523--526},
      NUMBER  = {{\bf 4}})

@ARTICLE(ENS_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Category {E}ns},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {527--533},
      NUMBER  = {{\bf 4}})

@ARTICLE(BORSUK_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {A {B}orsuk Theorem on Homotopy Types},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {535--545},
      NUMBER  = {{\bf 4}})

@ARTICLE(FUNCT_6.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {{C}artesian Product of Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {547--552},
      NUMBER  = {{\bf 4}})

@ARTICLE(MODAL_1.ABS,
      AUTHOR  = {de la Cruz, Alicia},
      TITLE   = {Introduction to Modal Propositional Logic},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {553--558},
      NUMBER  = {{\bf 4}})

@ARTICLE(TBSP_1.ABS,
      AUTHOR  = {de la Cruz, Alicia},
      TITLE   = {Totally Bounded Metric Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {559--562},
      NUMBER  = {{\bf 4}})

@ARTICLE(GRCAT_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Categories of Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {563--571},
      NUMBER  = {{\bf 4}})

@ARTICLE(GROUP_6.ABS,
      AUTHOR  = {Trybulec, Wojciech A. and Trybulec, Micha{\l} J.},
      TITLE   = {Homomorphisms and Isomorphisms of Groups. {Q}uotient Group},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {573--578},
      NUMBER  = {{\bf 4}})

@ARTICLE(MOD_2.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Rings and Modules -- Part {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {579--585},
      NUMBER  = {{\bf 4}})

@ARTICLE(MOD_3.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Free Modules},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {587--589},
      NUMBER  = {{\bf 4}})

@ARTICLE(ANALORT.ABS,
      AUTHOR  = {Zajkowski, Jaros{\l}aw},
      TITLE   = {Oriented Metric-Affine Plane -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {591--597},
      NUMBER  = {{\bf 4}})

@ARTICLE(EUCLID.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata},
      TITLE   = {The {E}uclidean Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {599--603},
      NUMBER  = {{\bf 4}})

@ARTICLE(TOPMETR.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata and Nakamura, Yatsuka},
      TITLE   = {Metric Spaces as Topological Spaces -- Fundamental Concepts},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {605--608},
      NUMBER  = {{\bf 4}})

@ARTICLE(HEINE.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata and Nakamura, Yatsuka},
      TITLE   = {{H}eine--{B}orel's Covering Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {609--610},
      NUMBER  = {{\bf 4}})

@ARTICLE(TOPMETR2.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Darmochwa{\l}, Agata},
      TITLE   = {Some Facts about Union of Two Functions and Continuity of Union of Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {611--613},
      NUMBER  = {{\bf 4}})

@ARTICLE(TOPREAL1.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata and Nakamura, Yatsuka},
      TITLE   = {The Topological Space ${\calE}^2_{\rmT}$. {A}rcs, Line Segments and Special Polygonal Arcs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {617--621},
      NUMBER  = {{\bf 5}})

@ARTICLE(GR_CY_1.ABS,
      AUTHOR  = {Surowik, Dariusz},
      TITLE   = {Cyclic Groups and Some of Their Properties -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {623--627},
      NUMBER  = {{\bf 5}})

@ARTICLE(ISOCAT_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Isomorphisms of Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {629--634},
      NUMBER  = {{\bf 5}})

@ARTICLE(CQC_SIM1.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata and Trybulec, Andrzej},
      TITLE   = {Similarity of Formulae},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {635--642},
      NUMBER  = {{\bf 5}})

@ARTICLE(RINGCAT1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Category of Rings},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {643--648},
      NUMBER  = {{\bf 5}})

@ARTICLE(MODCAT_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Category of Left Modules},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {649--652},
      NUMBER  = {{\bf 5}})

@ARTICLE(FDIFF_3.ABS,
      AUTHOR  = {Burakowska, Ewa and Madras, Beata},
      TITLE   = {Real Function One-Side Differentiability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {653--656},
      NUMBER  = {{\bf 5}})

@ARTICLE(METRIC_6.ABS,
      AUTHOR  = {Kanas, Stanis{\l}awa and Lecko, Adam},
      TITLE   = {Sequences in Metric Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {657--661},
      NUMBER  = {{\bf 5}})

@ARTICLE(TOPREAL2.ABS,
      AUTHOR  = {Darmochwa{\l}, Agata and Nakamura, Yatsuka},
      TITLE   = {The Topological Space ${\calE}^2_{\rmT}$. {S}imple Closed Curves},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {663--664},
      NUMBER  = {{\bf 5}})

@ARTICLE(TSEP_1.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {Separated and Weakly Separated Subspaces of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {665--674},
      NUMBER  = {{\bf 5}})

@ARTICLE(L_HOSPIT.ABS,
      AUTHOR  = {Korolkiewicz, Ma{\l}gorzata},
      TITLE   = {The de l'{H}ospital Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {675--678},
      NUMBER  = {{\bf 5}})

@ARTICLE(COMMACAT.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Darmochwa\l, Agata},
      TITLE   = {Comma Category},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {679--681},
      NUMBER  = {{\bf 5}})

@ARTICLE(LANG1.ABS,
      AUTHOR  = {Carlson, Patricia L. and Bancerek, Grzegorz},
      TITLE   = {Context-Free Grammar -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {683--687},
      NUMBER  = {{\bf 5}})

@ARTICLE(MEASURE3.ABS,
      AUTHOR  = {Bia{\l}as, J\'ozef},
      TITLE   = {Completeness of the $\sigma$-Additive Measure. {M}easure Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {689--693},
      NUMBER  = {{\bf 5}})

@ARTICLE(BHSP_4.ABS,
      AUTHOR  = {Kraszewska, El\.zbieta and Popio{\l}ek, Jan},
      TITLE   = {Series in {B}anach and {H}ilbert {S}paces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {695--699},
      NUMBER  = {{\bf 5}})

@ARTICLE(CAT_3.ABS,
      AUTHOR  = {Byli\'{n}ski, Czes{\l}aw},
      TITLE   = {Products and Coproducts in Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {701--709},
      NUMBER  = {{\bf 5}})

@ARTICLE(MATRIX_2.ABS,
      AUTHOR  = {Jankowska, Katarzyna},
      TITLE   = {Transpose Matrices and Groups of Permutations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {711--717},
      NUMBER  = {{\bf 5}})

@ARTICLE(LATTICE3.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Complete Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1991},
      VOLUME  = 2,
      PAGES   = {719--725},
      NUMBER  = {{\bf 5}})

@ARTICLE(TMAP_1.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {Continuity of Mappings over the Union  of Subspaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {1--16},
      NUMBER  = {{\bf 1}})

@ARTICLE(SEQFUNC.ABS,
      AUTHOR  = {Perkowska, Beata},
      TITLE   = {Functional Sequence from a Domain to a Domain},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {17--21},
      NUMBER  = {{\bf 1}})

@ARTICLE(MIDSP_3.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Reper Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {23--28},
      NUMBER  = {{\bf 1}})

@ARTICLE(GR_CY_2.ABS,
      AUTHOR  = {Surowik, Dariusz},
      TITLE   = {Isomorphisms of Cyclic Groups. {S}ome Properties of Cyclic Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {29--32},
      NUMBER  = {{\bf 1}})

@ARTICLE(ISOCAT_2.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Some Isomorphisms Between Functor Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {33--40},
      NUMBER  = {{\bf 1}})

@ARTICLE(TDLAT_1.ABS,
      AUTHOR  = {Watanabe, Toshihiko},
      TITLE   = {The Lattice of Domains of a Topological Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {41--46},
      NUMBER  = {{\bf 1}})

@ARTICLE(LMOD_6.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Submodules},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {47--51},
      NUMBER  = {{\bf 1}})

@ARTICLE(DIRORT.ABS,
      AUTHOR  = {Zajkowski, Jaros{\l}aw},
      TITLE   = {Oriented Metric-Affine Plane -- Part {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {53--56},
      NUMBER  = {{\bf 1}})

@ARTICLE(MOD_4.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Opposite Rings, Modules and their Morphisms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {57--65},
      NUMBER  = {{\bf 1}})

@ARTICLE(MEASURE4.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {Properties of {C}aratheodor's Measure},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {67--70},
      NUMBER  = {{\bf 1}})

@ARTICLE(TDLAT_2.ABS,
      AUTHOR  = {Karno, Zbigniew and Watanabe, Toshihiko},
      TITLE   = {Completeness of the Lattices of Domains  of a Topological Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {71--79},
      NUMBER  = {{\bf 1}})

@ARTICLE(PCOMPS_2.ABS,
      AUTHOR  = {Borys, Leszek},
      TITLE   = {On Paracompactness of Metrizable Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {81--84},
      NUMBER  = {{\bf 1}})

@ARTICLE(TREAL_1.ABS,
      AUTHOR  = {Watanabe, Toshihiko},
      TITLE   = {The {B}rouwer Fixed Point Theorem for Intervals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {85--88},
      NUMBER  = {{\bf 1}})

@ARTICLE(CARD_5.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {On Powers of Cardinals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {89--93},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPREAL3.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Kotowicz, Jaros{\l}aw},
      TITLE   = {Basic Properties of Connecting Points with Line Segments in ${\calE}^2_{\rmT}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {95--99},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPREAL4.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Kotowicz, Jaros{\l}aw},
      TITLE   = {Connectedness Conditions Using Polygonal Arcs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {101--106},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOBOARD1.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Nakamura, Yatsuka},
      TITLE   = {Introduction to {G}o-Board -- Part {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {107--115},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOBOARD2.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Nakamura, Yatsuka},
      TITLE   = {Introduction to {G}o-Board -- Part {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {117--121},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOBOARD3.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Nakamura, Yatsuka},
      TITLE   = {Properties of {G}o-Board -- Part {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {123--124},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOBOARD4.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Nakamura, Yatsuka},
      TITLE   = {Go-Board Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {125--129},
      NUMBER  = {{\bf 1}})

@ARTICLE(SYSREL.ABS,
      AUTHOR  = {Korczy\'nski, Waldemar},
      TITLE   = {Some Properties of Binary Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {131--134},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN1.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Kotowicz, Jaros{\l}aw},
      TITLE   = {The {J}ordan's Property for Certain Subsets of the Plane},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {137--142},
      NUMBER  = {{\bf 2}})

@ARTICLE(TDLAT_3.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {The Lattice of Domains of an Extremally Disconnected Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {143--149},
      NUMBER  = {{\bf 2}})

@ARTICLE(AMI_1.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {A Mathematical Model of {CPU}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {151--160},
      NUMBER  = {{\bf 2}})

@ARTICLE(CAT_4.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {{C}artesian Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {161--169},
      NUMBER  = {{\bf 2}})

@ARTICLE(VFUNCT_1.ABS,
      AUTHOR  = {Yamazaki, Hiroshi and Shidama, Yasunari},
      TITLE   = {Algebra of Vector Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {171--175},
      NUMBER  = {{\bf 2}})

@ARTICLE(TSEP_2.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {On a Duality between Weakly Separated  Subspaces of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {177--182},
      NUMBER  = {{\bf 2}})

@ARTICLE(PETRI.ABS,
      AUTHOR  = {Kawamoto, Pauline N. and Fuwa, Yasushi and Nakamura, Yatsuka},
      TITLE   = {Basic {P}etri Net Concepts},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {183--187},
      NUMBER  = {{\bf 2}})

@ARTICLE(FIN_TOPO.ABS,
      AUTHOR  = {Imura, Hiroshi and Eguchi, Masayoshi},
      TITLE   = {Finite Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {189--193},
      NUMBER  = {{\bf 2}})

@ARTICLE(TREES_3.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Sets and Functions of Trees and Joining Operations of Trees},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {195--204},
      NUMBER  = {{\bf 2}})

@ARTICLE(FVSUM_1.ABS,
      AUTHOR  = {Zawadzka, Katarzyna},
      TITLE   = {The Sum and Product of Finite Sequences of Elements of a Field},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {205--211},
      NUMBER  = {{\bf 2}})

@ARTICLE(MONOID_0.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Monoids},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {213--225},
      NUMBER  = {{\bf 2}})

@ARTICLE(MONOID_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Monoid of Multisets and Subsets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {227--233},
      NUMBER  = {{\bf 2}})

@ARTICLE(PRVECT_1.ABS,
      AUTHOR  = {Lango, Anna and Bancerek, Grzegorz},
      TITLE   = {Product of Families of Groups and Vector Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {235--240},
      NUMBER  = {{\bf 2}})

@ARTICLE(AMI_2.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {On a Mathematical Model of Programs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {241--250},
      NUMBER  = {{\bf 2}})

@ARTICLE(UNIALG_1.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Madras, Beata and Korolkiewicz, Ma{\l}gorzata},
      TITLE   = {Basic Notation of Universal Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {251--253},
      NUMBER  = {{\bf 2}})

@ARTICLE(COH_SP.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Raczkowski, Konrad},
      TITLE   = {Coherent Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {255--261},
      NUMBER  = {{\bf 2}})

@ARTICLE(MEASURE5.ABS,
      AUTHOR  = {Bia{\l}as, J\'{o}zef},
      TITLE   = {Properties of the Intervals of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {263--269},
      NUMBER  = {{\bf 2}})

@ARTICLE(RLVECT_4.ABS,
      AUTHOR  = {Trybulec, Wojciech A.},
      TITLE   = {Subspaces of Real Linear Space generated by One, Two, or Three        Vectors and Their Cosets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {271--274},
      NUMBER  = {{\bf 2}})

@ARTICLE(RFINSEQ.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Functions and Finite Sequences of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {275--278},
      NUMBER  = {{\bf 2}})

@ARTICLE(RFUNCT_3.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw and Sakai, Yuji},
      TITLE   = {Properties of Partial Functions from a Domain to the Set of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {279--288},
      NUMBER  = {{\bf 2}})

@ARTICLE(LMOD_7.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Domains of Submodules, Join and Meet of Finite Sequences of Submodules and Quotient Modules},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {289--296},
      NUMBER  = {{\bf 2}})

@ARTICLE(TOPS_3.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {Remarks on Special Subsets of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {297--303},
      NUMBER  = {{\bf 2}})

@ARTICLE(TEX_1.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {On Discrete and Almost Discrete Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1992},
      VOLUME  = 3,
      PAGES   = {305--310},
      NUMBER  = {{\bf 2}})

@ARTICLE(MATRIX_3.ABS,
      AUTHOR  = {Zawadzka, Katarzyna},
      TITLE   = {The Product and the Determinant of Matrices with Entries in a Field},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {1--8},
      NUMBER  = {{\bf 1}})

@ARTICLE(REARRAN1.ABS,
      AUTHOR  = {Sakai, Yuji and Kotowicz, Jaros{\l}aw},
      TITLE   = {Introduction to Theory of Rearrangement},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {9--13},
      NUMBER  = {{\bf 1}})

@ARTICLE(PBOOLE.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Many-sorted Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {15--22},
      NUMBER  = {{\bf 1}})

@ARTICLE(UNIALG_2.ABS,
      AUTHOR  = {Burakowska, Ewa},
      TITLE   = {Subalgebras of the Universal Algebra. {L}attices of Subalgebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {23--27},
      NUMBER  = {{\bf 1}})

@ARTICLE(HAHNBAN.ABS,
      AUTHOR  = {Nowak, Bogdan and Trybulec, Andrzej},
      TITLE   = {Hahn-{B}anach Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {29--34},
      NUMBER  = {{\bf 1}})

@ARTICLE(LATTICE4.ABS,
      AUTHOR  = {Kamie{\'n}ska, Jolanta and Walijewski, Jaros{\l}aw Stanis{\l}aw},
      TITLE   = {Homomorphisms of Lattices, Finite Join and Finite Meet},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {35--40},
      NUMBER  = {{\bf 1}})

@ARTICLE(OPENLATT.ABS,
      AUTHOR  = {Kamie\'nska, Jolanta},
      TITLE   = {Representation Theorem for {H}eyting Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {41--45},
      NUMBER  = {{\bf 1}})

@ARTICLE(LOPCLSET.ABS,
      AUTHOR  = {Walijewski, Jaros{\l}aw Stanis{\l}aw},
      TITLE   = {Representation Theorem for Boolean Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {45--50},
      NUMBER  = {{\bf 1}})

@ARTICLE(AMI_3.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {Some Remarks on the Simple Concrete Model of Computer},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {51--56},
      NUMBER  = {{\bf 1}})

@ARTICLE(AMI_4.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {{E}uclid's Algorithm},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {57--60},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCM_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Rudnicki, Piotr},
      TITLE   = {Development of Terminology for {\SCM}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {61--67},
      NUMBER  = {{\bf 1}})

@ARTICLE(PRE_FF.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Rudnicki, Piotr},
      TITLE   = {Two Programs for {\SCM}. {P}art {I} -- Preliminaries},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {69--72},
      NUMBER  = {{\bf 1}})

@ARTICLE(FIB_FUSC.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Rudnicki, Piotr},
      TITLE   = {Two Programs for {\SCM}. {P}art {II} -- Programs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {73--75},
      NUMBER  = {{\bf 1}})

@ARTICLE(TREES_4.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Joining of Decorated Trees},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {77--82},
      NUMBER  = {{\bf 1}})

@ARTICLE(BINARITH.ABS,
      AUTHOR  = {Nishiyama, Takaya and Mizuhara, Yasuho},
      TITLE   = {Binary Arithmetics},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {83--86},
      NUMBER  = {{\bf 1}})

@ARTICLE(BOOLMARK.ABS,
      AUTHOR  = {Kawamoto, Pauline N. and Fuwa, Yasushi and Nakamura, Yatsuka},
      TITLE   = {Basic Concepts for {P}etri Nets with Boolean Markings},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {87--90},
      NUMBER  = {{\bf 1}})

@ARTICLE(DTCONSTR.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Rudnicki, Piotr},
      TITLE   = {On Defining Functions on Trees},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {91--101},
      NUMBER  = {{\bf 1}})

@ARTICLE(PRALG_1.ABS,
      AUTHOR  = {Madras, Beata},
      TITLE   = {Product of Family of Universal Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {103--108},
      NUMBER  = {{\bf 1}})

@ARTICLE(ALG_1.ABS,
      AUTHOR  = {Korolkiewicz, Ma{\l}gorzata},
      TITLE   = {Homomorphisms of Algebras. {Q}uotient Universal Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {109--113},
      NUMBER  = {{\bf 1}})

@ARTICLE(FREEALG.ABS,
      AUTHOR  = {Perkowska, Beata},
      TITLE   = {Free Universal Algebra Construction},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {115--120},
      NUMBER  = {{\bf 1}})

@ARTICLE(COMSEQ_1.ABS,
      AUTHOR  = {Banachowicz, Agnieszka and Winnicka, Anna},
      TITLE   = {Complex Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {121--124},
      NUMBER  = {{\bf 1}})

@ARTICLE(TEX_2.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {Maximal Discrete Subspaces of Almost Discrete Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {125--135},
      NUMBER  = {{\bf 1}})

@ARTICLE(TEX_3.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {On Nowhere and Everywhere Dense Subspaces of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1993},
      VOLUME  = 4,
      PAGES   = {137--146},
      NUMBER  = {{\bf 1}})

@ARTICLE(AMI_5.ABS,
      AUTHOR  = {Tanaka, Yasushi},
      TITLE   = {On the Decomposition of the States of {SCM}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {1--8},
      NUMBER  = {{\bf 1}})

@ARTICLE(BINTREE1.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Rudnicki, Piotr},
      TITLE   = {On Defining Functions on Binary Trees},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {9--13},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCM_COMP.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Rudnicki, Piotr},
      TITLE   = {A Compiler of Arithmetic Expressions for {SCM}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {15--20},
      NUMBER  = {{\bf 1}})

@ARTICLE(MEASURE6.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {Some Properties of the Intervals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {21--26},
      NUMBER  = {{\bf 1}})

@ARTICLE(BINARI_2.ABS,
      AUTHOR  = {Mizuhara, Yasuho and Nishiyama, Takaya},
      TITLE   = {Binary Arithmetics, Addition and Subtraction of Integers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {27--29},
      NUMBER  = {{\bf 1}})

@ARTICLE(BOOLEALG.ABS,
      AUTHOR  = {Marasik, Agnieszka Julia},
      TITLE   = {Boolean Properties of Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {31--35},
      NUMBER  = {{\bf 1}})

@ARTICLE(MSUALG_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Many Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {37--42},
      NUMBER  = {{\bf 1}})

@ARTICLE(AUTGROUP.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Group of Inner Automorphisms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {43--45},
      NUMBER  = {{\bf 1}})

@ARTICLE(MSUALG_2.ABS,
      AUTHOR  = {Burakowska, Ewa},
      TITLE   = {Subalgebras of Many Sorted Algebra. {L}attice of Subalgebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {47--54},
      NUMBER  = {{\bf 1}})

@ARTICLE(PRALG_2.ABS,
      AUTHOR  = {Madras, Beata},
      TITLE   = {Products of Many Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {55--60},
      NUMBER  = {{\bf 1}})

@ARTICLE(MSUALG_3.ABS,
      AUTHOR  = {Korolkiewicz, Ma{\l}gorzata},
      TITLE   = {Homomorphisms of Many Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {61--65},
      NUMBER  = {{\bf 1}})

@ARTICLE(MSAFREE.ABS,
      AUTHOR  = {Perkowska, Beata},
      TITLE   = {Free Many Sorted Universal Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {67--74},
      NUMBER  = {{\bf 1}})

@ARTICLE(T_0TOPSP.ABS,
      AUTHOR  = {\.Zynel, Mariusz and Guzowski, Adam},
      TITLE   = { \Tzero\ Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {75--77},
      NUMBER  = {{\bf 1}})

@ARTICLE(MSUALG_4.ABS,
      AUTHOR  = {Korolkiewicz, Ma{\l}gorzata},
      TITLE   = {Many Sorted Quotient Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {79--84},
      NUMBER  = {{\bf 1}})

@ARTICLE(QUANTAL1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Quantales},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {85--91},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPRNS_1.ABS,
      AUTHOR  = {Sakowicz, Agnieszka and Gryko, Jaros{\l}aw and Grabowski, Adam},
      TITLE   = {Sequences in ${\calE}^{N}_{\rmT}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {93--96},
      NUMBER  = {{\bf 1}})

@ARTICLE(SPPOL_1.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Byli\'nski, Czes\l{}aw},
      TITLE   = {Extremal Properties of Vertices on Special Polygons. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {97--102},
      NUMBER  = {{\bf 1}})

@ARTICLE(RELOC.ABS,
      AUTHOR  = {Tanaka, Yasushi},
      TITLE   = {Relocatability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {103--108},
      NUMBER  = {{\bf 1}})

@ARTICLE(TEX_4.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {Maximal Anti-Discrete Subspaces of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {109--118},
      NUMBER  = {{\bf 1}})

@ARTICLE(TSP_1.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {On {K}olmogorov Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {119--124},
      NUMBER  = {{\bf 1}})

@ARTICLE(TSP_2.ABS,
      AUTHOR  = {Karno, Zbigniew},
      TITLE   = {Maximal {K}olmogorov Subspaces of a Topological Space as {S}tone Retracts of the Ambient Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {125--130},
      NUMBER  = {{\bf 1}})

@ARTICLE(PROJPL_1.ABS,
      AUTHOR  = {Muzalewski, Micha{\l}},
      TITLE   = {Projective Planes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {131--136},
      NUMBER  = {{\bf 1}})

@ARTICLE(SGRAPH1.ABS,
      AUTHOR  = {Toda, Yozo},
      TITLE   = {The Formalization of Simple Graphs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {137--144},
      NUMBER  = {{\bf 1}})

@ARTICLE(GRSOLV_1.ABS,
      AUTHOR  = {Zawadzka, Katarzyna},
      TITLE   = {Solvable Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {145--147},
      NUMBER  = {{\bf 1}})

@ARTICLE(FILTER_2.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Ideals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {149--156},
      NUMBER  = {{\bf 2}})

@ARTICLE(CAT_5.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Categorial Categories and Slice Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {157--165},
      NUMBER  = {{\bf 2}})

@ARTICLE(PRE_CIRC.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Rudnicki, Piotr and Trybulec, Andrzej and Kawamoto, Pauline N.},
      TITLE   = {Preliminaries to Circuits, {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {167--172},
      NUMBER  = {{\bf 2}})

@ARTICLE(FSM_1.ABS,
      AUTHOR  = {Kaloper , Miroslava and Rudnicki, Piotr},
      TITLE   = {Minimization of finite state machines},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {173--184},
      NUMBER  = {{\bf 2}})

@ARTICLE(TREES_9.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Subtrees},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {185--190},
      NUMBER  = {{\bf 2}})

@ARTICLE(MSATERM.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Terms Over Many Sorted Universal Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {191--198},
      NUMBER  = {{\bf 2}})

@ARTICLE(DECOMP_1.ABS,
      AUTHOR  = {Przemski, Marian},
      TITLE   = {On the Decomposition of the Continuity},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {199--204},
      NUMBER  = {{\bf 2}})

@ARTICLE(MSAFREE1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {A Scheme for Extensions of Homomorphisms of Manysorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {205--209},
      NUMBER  = {{\bf 2}})

@ARTICLE(MSUHOM_1.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {The Correspondence Between Homomorphisms of Universal Algebra   \& Many Sorted Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {211--214},
      NUMBER  = {{\bf 2}})

@ARTICLE(MSAFREE2.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Rudnicki, Piotr and Trybulec, Andrzej and Kawamoto, Pauline N.},
      TITLE   = {Preliminaries to Circuits, {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {215--220},
      NUMBER  = {{\bf 2}})

@ARTICLE(AUTALG_1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Group of Automorphisms of Universal Algebra \&         Many Sorted Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {221--226},
      NUMBER  = {{\bf 2}})

@ARTICLE(CIRCUIT1.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Rudnicki, Piotr and Trybulec, Andrzej and Kawamoto, Pauline N.},
      TITLE   = {Introduction to Circuits, {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {227--232},
      NUMBER  = {{\bf 2}})

@ARTICLE(CANTOR_1.ABS,
      AUTHOR  = {Shibakov, Alexander Yu. and Trybulec, Andrzej},
      TITLE   = {The {C}antor Set},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {233--236},
      NUMBER  = {{\bf 2}})

@ARTICLE(CQC_THE3.ABS,
      AUTHOR  = {Okhotnikov, Oleg},
      TITLE   = {Logical Equivalence of Formulae},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {237--240},
      NUMBER  = {{\bf 2}})

@ARTICLE(FINSEQ_5.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Some Properties of Restrictions of Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {241--245},
      NUMBER  = {{\bf 2}})

@ARTICLE(SPPOL_2.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw and Nakamura, Yatsuka},
      TITLE   = {Special Polygons},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {247--252},
      NUMBER  = {{\bf 2}})

@ARTICLE(MEASURE7.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef},
      TITLE   = {The One-Dimensional {L}ebesgue Measure},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {253--258},
      NUMBER  = {{\bf 2}})

@ARTICLE(ALTCAT_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Categories without Uniqueness of {\bf cod} and {\bf dom}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {259--267},
      NUMBER  = {{\bf 2}})

@ARTICLE(EXTENS_1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Extensions of Mappings on Generator Set},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {269--272},
      NUMBER  = {{\bf 2}})

@ARTICLE(CIRCUIT2.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Rudnicki, Piotr and Trybulec, Andrzej and Kawamoto, Pauline N.},
      TITLE   = {Introduction to Circuits, {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {273--278},
      NUMBER  = {{\bf 2}})

@ARTICLE(MBOOLEAN.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Definitions and Basic Properties of Boolean \& Union of Many Sorted Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {279--281},
      NUMBER  = {{\bf 2}})

@ARTICLE(CIRCCOMB.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Bancerek, Grzegorz},
      TITLE   = {Combining of Circuits},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {283--295},
      NUMBER  = {{\bf 2}})

@ARTICLE(GRAPH_2.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Rudnicki, Piotr},
      TITLE   = {Vertex Sequences Induced by Chains},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {297--304},
      NUMBER  = {{\bf 3}})

@ARTICLE(VECTSP_8.ABS,
      AUTHOR  = {Iwaniuk, Andrzej},
      TITLE   = {On the Lattice of Subspaces of a Vector Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {305--308},
      NUMBER  = {{\bf 3}})

@ARTICLE(LATSUBGR.ABS,
      AUTHOR  = {Ganczarski, Janusz},
      TITLE   = {On the Lattice of Subgroups of a Group},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {309--312},
      NUMBER  = {{\bf 3}})

@ARTICLE(UNIALG_3.ABS,
      AUTHOR  = {Paszek, Miros{\l}aw Jan},
      TITLE   = {On the Lattice of Subalgebras of a Universal Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {313--316},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINSEQ_6.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {On the Decomposition of Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {317--322},
      NUMBER  = {{\bf 3}})

@ARTICLE(GOBOARD5.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {Decomposing a {G}o-Board into Cells},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {323--328},
      NUMBER  = {{\bf 3}})

@ARTICLE(INDEX_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Indexed Category},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {329--337},
      NUMBER  = {{\bf 3}})

@ARTICLE(MATRLIN.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Associated Matrix of Linear Map},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {339--345},
      NUMBER  = {{\bf 3}})

@ARTICLE(GOBOARD6.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {On the Geometry of a {G}o-{B}oard},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {347--352},
      NUMBER  = {{\bf 3}})

@ARTICLE(WEIERSTR.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef and Nakamura, Yatsuka},
      TITLE   = {The Theorem of {W}eierstrass},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {353--359},
      NUMBER  = {{\bf 3}})

@ARTICLE(URYSOHN1.ABS,
      AUTHOR  = {Bia{\l}as, J{\'o}zef and Nakamura, Yatsuka},
      TITLE   = {Dyadic Numbers and {T}${}_4$ Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {361--366},
      NUMBER  = {{\bf 3}})

@ARTICLE(FACIRC_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Nakamura, Yatsuka},
      TITLE   = {Full Adder Circuit.  {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {367--380},
      NUMBER  = {{\bf 3}})

@ARTICLE(COHSP_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Continuous, Stable, and Linear Maps of Coherence Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {381--393},
      NUMBER  = {{\bf 3}})

@ARTICLE(PZFMISC1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Some Basic Properties of Many Sorted Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {395--399},
      NUMBER  = {{\bf 3}})

@ARTICLE(TREES_A.ABS,
      AUTHOR  = {Okhotnikov, Oleg},
      TITLE   = {Replacement of Subtrees in a Tree},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {401--403},
      NUMBER  = {{\bf 3}})

@ARTICLE(PUA2MSS1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Minimal Signature for Partial Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {405--414},
      NUMBER  = {{\bf 3}})

@ARTICLE(QC_LANG4.ABS,
      AUTHOR  = {Okhotnikov, Oleg},
      TITLE   = {The Subformula Tree of a Formula of the First Order Language},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {415--422},
      NUMBER  = {{\bf 3}})

@ARTICLE(VECTSP_9.ABS,
      AUTHOR  = {{\.Z}ynel, Mariusz},
      TITLE   = {The {S}teinitz Theorem and the Dimension of a Vector Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {423--428},
      NUMBER  = {{\bf 3}})

@ARTICLE(GOBOARD7.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {On the {G}o-{B}oard of a Standard Special Circular Sequence},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {429--438},
      NUMBER  = {{\bf 3}})

@ARTICLE(ENDALG.ABS,
      AUTHOR  = {Gryko, Jaros{\l}aw},
      TITLE   = {On the Monoid of Endomorphisms of Universal Algebra and Many Sorted Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {439--442},
      NUMBER  = {{\bf 3}})

@ARTICLE(GOBOARD8.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {More on Segments on a {G}o-{B}oard},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {443--450},
      NUMBER  = {{\bf 3}})

@ARTICLE(MSSUBFAM.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Certain Facts about Families of Subsets of Many Sorted Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {451--456},
      NUMBER  = {{\bf 3}})

@ARTICLE(TRIANG_1.ABS,
      AUTHOR  = {Madras, Beata},
      TITLE   = {On the Concept of the Triangulation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {457--462},
      NUMBER  = {{\bf 3}})

@ARTICLE(GOBOARD9.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Left and Right Component of the Complement of a Special Closed Curve},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {465--468},
      NUMBER  = {{\bf 4}})

@ARTICLE(REWRITE1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Reduction Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {469--478},
      NUMBER  = {{\bf 4}})

@ARTICLE(MSUALG_5.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Lattice of Congruences in Many Sorted Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {479--483},
      NUMBER  = {{\bf 4}})

@ARTICLE(FUNCT_7.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Trybulec, Andrzej},
      TITLE   = {Miscellaneous Facts about Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {485--492},
      NUMBER  = {{\bf 4}})

@ARTICLE(ALTCAT_2.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Examples of Category Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {493--500},
      NUMBER  = {{\bf 4}})

@ARTICLE(ORDERS_3.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {On the Category of Posets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {501--505},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA_1.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka and Rudnicki, Piotr},
      TITLE   = {An Extension of {\SCM}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {507--512},
      NUMBER  = {{\bf 4}})

@ARTICLE(CONNSP_3.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {Components and Unions of Components},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {513--517},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA_2.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka and Rudnicki, Piotr},
      TITLE   = {The {\SCMFSA} Computer},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {519--528},
      NUMBER  = {{\bf 4}})

@ARTICLE(CLOSURE1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Many Sorted Closure Operator and the Many Sorted Closure System},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {529--536},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA_3.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {Computation in {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {537--542},
      NUMBER  = {{\bf 4}})

@ARTICLE(CLOSURE2.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Closure Operator and the Closure System of Many Sorted Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {543--551},
      NUMBER  = {{\bf 4}})

@ARTICLE(MSUALG_6.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Translations, Endomorphisms, and Stable Equational Theories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {553--564},
      NUMBER  = {{\bf 4}})

@ARTICLE(MSUALG_7.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {More on the Lattice of Many Sorted Equivalence Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {565--569},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA_4.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {Modifying Addresses of Instructions of {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {571--576},
      NUMBER  = {{\bf 4}})

@ARTICLE(MSSCYC_1.ABS,
      AUTHOR  = {Byli\'nski, Czes{\l}aw and Rudnicki, Piotr},
      TITLE   = {The Correspondence Between Monotonic Many Sorted Signatures and Well-Founded Graphs. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {577--582},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA_5.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {Relocability for {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {583--586},
      NUMBER  = {{\bf 4}})

@ARTICLE(MSUALG_8.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {More on the Lattice of Congruences in Many Sorted Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {587--590},
      NUMBER  = {{\bf 4}})

@ARTICLE(MSSCYC_2.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw and Rudnicki, Piotr},
      TITLE   = {The Correspondence Between Monotonic Many Sorted Signatures and Well-Founded Graphs. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {591--593},
      NUMBER  = {{\bf 4}})

@ARTICLE(FUNCTOR0.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Functors for Alternative Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {595--608},
      NUMBER  = {{\bf 4}})

@ARTICLE(FUNCTOR1.ABS,
      AUTHOR  = {Zinn, Claus and Jaksch, Wolfgang},
      TITLE   = {Basic Properties of Functor Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {609--613},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA_7.ABS,
      AUTHOR  = {Asamoto, Noriko},
      TITLE   = {Some Multi Instructions Defined by Sequence of Instructions of {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {615--619},
      NUMBER  = {{\bf 4}})

@ARTICLE(PRALG_3.ABS,
      AUTHOR  = {Giero, Mariusz},
      TITLE   = {More on Products of Many Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1996},
      VOLUME  = 5,
      PAGES   = {621--626},
      NUMBER  = {{\bf 4}})

@ARTICLE(GOBRD10.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {Adjacency Concept for Pairs of Natural Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {1--3},
      NUMBER  = {{\bf 1}})

@ARTICLE(MSALIMIT.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Inverse Limits of Many Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {5--8},
      NUMBER  = {{\bf 1}})

@ARTICLE(MSUALG_9.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Trivial Many Sorted Algebras and Many Sorted Congruences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {9--15},
      NUMBER  = {{\bf 1}})

@ARTICLE(MSINST_1.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Examples of Category Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {17--20},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMFSA6A.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka and Asamoto, Noriko},
      TITLE   = {On the Compositions of Macro Instructions. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {21--27},
      NUMBER  = {{\bf 1}})

@ARTICLE(SF_MASTR.ABS,
      AUTHOR  = {Rudnicki, Piotr and Trybulec, Andrzej},
      TITLE   = {Memory Handling for {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {29--36},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOBRD11.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {Some Topological Properties of Cells in ${\calE}^2_{\rmT}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {37--40},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMFSA6B.ABS,
      AUTHOR  = {Asamoto, Noriko and Nakamura, Yatsuka and Rudnicki, Piotr and Trybulec, Andrzej},
      TITLE   = {On the Composition of Macro Instructions. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {41--47},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOBRD12.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {The First Part of {J}ordan's Theorem for Special Polygons},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {49--51},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMFSA6C.ABS,
      AUTHOR  = {Asamoto, Noriko and Nakamura, Yatsuka and Rudnicki, Piotr and Trybulec, Andrzej},
      TITLE   = {On the Composition of Macro Instructions. {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {53--57},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMFSA7B.ABS,
      AUTHOR  = {Asamoto, Noriko},
      TITLE   = {Constant Assignment Macro Instructions of {\SCMFSA}. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {59--63},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMFSA8A.ABS,
      AUTHOR  = {Asamoto, Noriko},
      TITLE   = {Conditional Branch Macro Instructions of {\SCMFSA}. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {65--72},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMFSA8B.ABS,
      AUTHOR  = {Asamoto, Noriko},
      TITLE   = {Conditional Branch Macro Instructions of {\SCMFSA}. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {73--80},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW_0.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Bounds in Posets and Relational Substructures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {81--91},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL_0.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Directed Sets, Nets, Ideals, Filters, and Maps},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {93--107},
      NUMBER  = {{\bf 1}})

@ARTICLE(KNASTER.ABS,
      AUTHOR  = {Rudnicki, Piotr and Trybulec, Andrzej},
      TITLE   = {Fixpoints in Complete Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {109--115},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW_1.ABS,
      AUTHOR  = {Grabowski, Adam and Milewski, Robert},
      TITLE   = {Boolean Posets, Posets under Inclusion and Products of Relational Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {117--121},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW_2.ABS,
      AUTHOR  = {{\.Z}ynel, Mariusz and Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Properties of Relational Structures, Posets, Lattices and Maps},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {123--130},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Galois Connections},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {131--143},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW_3.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Cartesian Products of Relations and Relational Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {145--152},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW_4.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Definitions and Properties of the Join and Meet of Subsets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {153--158},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL_2.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Meet--Continuous Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {159--167},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL_3.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {The ``Way-Below'' Relation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {169--176},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL_4.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Auxiliary and Approximating Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {179--188},
      NUMBER  = {{\bf 2}})

@ARTICLE(TWOSCOMP.ABS,
      AUTHOR  = {Wasaki, Katsumi and Kawamoto, Pauline N.},
      TITLE   = {2's Complement Circuit},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {189--197},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL_5.ABS,
      AUTHOR  = {{\.Z}ynel, Mariusz},
      TITLE   = {The Equational Characterization of Continuous Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {199--205},
      NUMBER  = {{\bf 2}})

@ARTICLE(YELLOW_5.ABS,
      AUTHOR  = {Marasik, Agnieszka Julia},
      TITLE   = {Miscellaneous Facts about Relation Structure},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {207--211},
      NUMBER  = {{\bf 2}})

@ARTICLE(YELLOW_6.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {{M}oore-{S}mith Convergence},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {213--225},
      NUMBER  = {{\bf 2}})

@ARTICLE(YELLOW_7.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Duality in Relation Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {227--232},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL_6.ABS,
      AUTHOR  = {Madras, Beata},
      TITLE   = {Irreducible and Prime Elements},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {233--239},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL_7.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Prime Ideals and Filters},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {241--247},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL_8.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Algebraic Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {249--254},
      NUMBER  = {{\bf 2}})

@ARTICLE(JORDAN3.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Matuszewski, Roman},
      TITLE   = {Reconstructions of Special Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {255--263},
      NUMBER  = {{\bf 2}})

@ARTICLE(COMSEQ_2.ABS,
      AUTHOR  = {Naumowicz, Adam},
      TITLE   = {Conjugate Sequences, Bounded Complex Sequences and    Convergent Complex Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {265--268},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL_9.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Topological Properties of Meet-Continuous Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {269--277},
      NUMBER  = {{\bf 2}})

@ARTICLE(INSTALG1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Institution of Many Sorted Algebras. {P}art {I}: Signature Reduct of an Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {279--287},
      NUMBER  = {{\bf 2}})

@ARTICLE(YELLOW_8.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {{B}aire Spaces, {S}ober Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {289--294},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL10.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Closure Operators and Subalgebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {295--301},
      NUMBER  = {{\bf 2}})

@ARTICLE(CATALG_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Algebra of Morphisms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {303--310},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL11.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {{S}cott Topology},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {311--319},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL12.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the {B}aire Category Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {321--327},
      NUMBER  = {{\bf 2}})

@ARTICLE(ALTCAT_3.ABS,
      AUTHOR  = {Madras, Beata},
      TITLE   = {Basic Properties of Objects and Morphisms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {329--334},
      NUMBER  = {{\bf 3}})

@ARTICLE(ABIAN.ABS,
      AUTHOR  = {Rudnicki, Piotr and Trybulec, Andrzej},
      TITLE   = {{A}bian's Fixed Point Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {335--338},
      NUMBER  = {{\bf 3}})

@ARTICLE(WELLFND1.ABS,
      AUTHOR  = {Rudnicki, Piotr and Trybulec, Andrzej},
      TITLE   = {On Same Equivalents of Well-foundedness},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {339--343},
      NUMBER  = {{\bf 3}})

@ARTICLE(WAYBEL13.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Algebraic and Arithmetic Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {345--349},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN4.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Matuszewski, Roman and Grabowski, Adam},
      TITLE   = {Subsequences of Standard Special Circular Sequences in ${\calE}^2_{\rmT}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {351--358},
      NUMBER  = {{\bf 3}})

@ARTICLE(SUBSTLAT.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Lattice of Substitutions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {359--361},
      NUMBER  = {{\bf 3}})

@ARTICLE(EQUATION.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Equations in Many Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {363--369},
      NUMBER  = {{\bf 3}})

@ARTICLE(FUNCTOR2.ABS,
      AUTHOR  = {Nieszczerzewski, Robert},
      TITLE   = {Category of Functors Between Alternative Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {371--375},
      NUMBER  = {{\bf 3}})

@ARTICLE(YONEDA_1.ABS,
      AUTHOR  = {Wojciechowski, Miros{\l}aw},
      TITLE   = {Yoneda Embedding},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {377--379},
      NUMBER  = {{\bf 3}})

@ARTICLE(GCD_1.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {The Correctness of the Generic Algorithms of {B}rown and {H}enrici Concerning Addition and Multiplication in Fraction Fields},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {381--388},
      NUMBER  = {{\bf 3}})

@ARTICLE(BIRKHOFF.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {{B}irkhoff Theorem for Many Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {389--395},
      NUMBER  = {{\bf 3}})

@ARTICLE(CLOSURE3.ABS,
      AUTHOR  = {Marasik, Agnieszka Julia},
      TITLE   = {Algebraic Operation on Subsets of Many Sorted Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {397--401},
      NUMBER  = {{\bf 3}})

@ARTICLE(COMSEQ_3.ABS,
      AUTHOR  = {Shidama, Yasunari and Korni{\l}owicz, Artur},
      TITLE   = {Convergence and the Limit of Complex Sequences. {S}eries},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {403--410},
      NUMBER  = {{\bf 3}})

@ARTICLE(RLVECT_5.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {The {S}teinitz Theorem and the Dimension of a Real Linear Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {411--415},
      NUMBER  = {{\bf 3}})

@ARTICLE(GRAPH_3.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Rudnicki, Piotr},
      TITLE   = {{E}uler Circuits and Paths},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {417--425},
      NUMBER  = {{\bf 3}})

@ARTICLE(PSCOMP_1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw and Rudnicki, Piotr},
      TITLE   = {Bounding Boxes for Compact Sets in ${\calE}^2$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {427--440},
      NUMBER  = {{\bf 3}})

@ARTICLE(WAYBEL14.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw and Rudnicki, Piotr},
      TITLE   = {The {S}cott Topology. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {441--446},
      NUMBER  = {{\bf 3}})

@ARTICLE(BORSUK_2.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Introduction to the Homotopy Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {449--454},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN5A.ABS,
      AUTHOR  = {Grabowski, Adam and Nakamura, Yatsuka},
      TITLE   = {Some Properties of Real Maps},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {455--459},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN5B.ABS,
      AUTHOR  = {Grabowski, Adam and Nakamura, Yatsuka},
      TITLE   = {The Ordering of Points on a Curve. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {461--465},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN5C.ABS,
      AUTHOR  = {Grabowski, Adam and Nakamura, Yatsuka},
      TITLE   = {The Ordering of Points on a Curve. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {467--473},
      NUMBER  = {{\bf 4}})

@ARTICLE(ALTCAT_4.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Categories Without Uniqueness of { \bf cod} and { \bf dom}. {S}ome Properties of the Morphisms and the Functors},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {475--481},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA8C.ABS,
      AUTHOR  = {Asamoto, Noriko},
      TITLE   = {The {\tt loop} and {\tt Times} Macroinstruction for {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {483--497},
      NUMBER  = {{\bf 4}})

@ARTICLE(WAYBEL15.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Algebraic and Arithmetic Lattices. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {499--503},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN2B.ABS,
      AUTHOR  = {Matuszewski, Roman and Nakamura, Yatsuka},
      TITLE   = {Projections in n-Dimensional {E}uclidean Space to Each Coordinates},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {505--509},
      NUMBER  = {{\bf 4}})

@ARTICLE(TOPREAL5.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {Intermediate Value Theorem and Thickness of Simple Closed Curves},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {511--514},
      NUMBER  = {{\bf 4}})

@ARTICLE(LATTICE5.ABS,
      AUTHOR  = {Gryko, Jaros{\l}aw},
      TITLE   = {The {J}\'onson's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {515--524},
      NUMBER  = {{\bf 4}})

@ARTICLE(UNIFORM1.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {{L}ebesgue's Covering Lemma, Uniform Continuity and Segmentation of Arcs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {525--529},
      NUMBER  = {{\bf 4}})

@ARTICLE(SPRECT_1.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {On the Rectangular Finite Sequences of the Points of the Plane},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {531--539},
      NUMBER  = {{\bf 4}})

@ARTICLE(SPRECT_2.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {On the Order on a Special Polygon},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {541--548},
      NUMBER  = {{\bf 4}})

@ARTICLE(EULER_1.ABS,
      AUTHOR  = {Fujisawa, Yoshinori and Fuwa, Yasushi},
      TITLE   = {The {E}uler's Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {549--551},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA_9.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {While Macro Instructions of {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {553--561},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN6.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {A Decomposition of a Simple Closed Curves and the Order of Their Points},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {563--572},
      NUMBER  = {{\bf 4}})

@ARTICLE(WSIERP_1.ABS,
      AUTHOR  = {Kondracki, Andrzej},
      TITLE   = {The {C}hinese {R}emainder {T}heorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1997},
      VOLUME  = 6,
      PAGES   = {573--577},
      NUMBER  = {{\bf 4}})

@ARTICLE(FUNCTOR3.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Composition of Functors and Transformations in Alternative   Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {1--7},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL16.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Completely-Irreducible Elements},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {9--12},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL17.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {{S}cott-Continuous Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {13--18},
      NUMBER  = {{\bf 1}})

@ARTICLE(NAT_2.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Natural Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {19--22},
      NUMBER  = {{\bf 1}})

@ARTICLE(BINARI_3.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Binary Arithmetics. {B}inary Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {23--26},
      NUMBER  = {{\bf 1}})

@ARTICLE(BINTREE2.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Full Trees},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {27--30},
      NUMBER  = {{\bf 1}})

@ARTICLE(T_1TOPSP.ABS,
      AUTHOR  = {{N}aumowicz, Adam and {\L}api{\'n}ski, Mariusz},
      TITLE   = {On \Tone\ Reflex of Topological Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {31--34},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW_9.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Bases and Refinements of Topologies},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {35--43},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW10.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Properties of Product of Relational Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {45--52},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW11.ABS,
      AUTHOR  = {Naumowicz, Adam},
      TITLE   = {On the Characterization of Modular and Distributive Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {53--55},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL18.ABS,
      AUTHOR  = {Gryko, Jaros{\l}aw},
      TITLE   = {Injective Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {57--62},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW12.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Characterization of {H}ausdorff Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {63--68},
      NUMBER  = {{\bf 1}})

@ARTICLE(QUOFIELD.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {The Field of Quotients Over an Integral Domain},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {69--79},
      NUMBER  = {{\bf 1}})

@ARTICLE(FRECHET.ABS,
      AUTHOR  = {Skorulski, Bart{\l}omiej},
      TITLE   = {First-countable, Sequential, and {F}rechet Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {81--86},
      NUMBER  = {{\bf 1}})

@ARTICLE(SFMASTR1.ABS,
      AUTHOR  = {Rudnicki, Piotr},
      TITLE   = {On the Composition of Non-parahalting Macro Instructions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {87--92},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMFSA9A.ABS,
      AUTHOR  = {Rudnicki, Piotr},
      TITLE   = {The {\tt while} Macro Instructions of {\SCMFSA}. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {93--100},
      NUMBER  = {{\bf 1}})

@ARTICLE(SFMASTR2.ABS,
      AUTHOR  = {Rudnicki, Piotr},
      TITLE   = {Another {\tt times} Macro Instruction},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {101--105},
      NUMBER  = {{\bf 1}})

@ARTICLE(SFMASTR3.ABS,
      AUTHOR  = {Rudnicki, Piotr},
      TITLE   = {The {\tt for} (going up) Macro Instruction},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {107--114},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN5D.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Grabowski, Adam},
      TITLE   = {Bounding Boxes for Special Sequences in ${\calE}^2$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {115--121},
      NUMBER  = {{\bf 1}})

@ARTICLE(EULER_2.ABS,
      AUTHOR  = {Fujisawa, Yoshinori and Fuwa, Yasushi and Shimizu, Hidetaka},
      TITLE   = {{E}uler's {T}heorem and Small {F}ermat's {T}heorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {123--126},
      NUMBER  = {{\bf 1}})

@ARTICLE(GROUP_7.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Product of the Families of the Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {127--134},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN7.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {On the Dividing Function of the Simple Closed Curve into Segments},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {135--138},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCM_HALT.ABS,
      AUTHOR  = {Chen, Jing-Chao and Nakamura, Yatsuka},
      TITLE   = {Initialization Halting Concepts and Their Basic Properties of {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {139--151},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMBSORT.ABS,
      AUTHOR  = {Chen, Jing-Chao and Nakamura, Yatsuka},
      TITLE   = {Bubble Sort on {\SCMFSA}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {153--161},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL19.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {The {L}awson Topology},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {163--168},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL20.ABS,
      AUTHOR  = {Rudnicki, Piotr},
      TITLE   = {Kernel Projections and Quotient Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {169--175},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL21.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {{L}awson Topology in Continuous Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {177--184},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL22.ABS,
      AUTHOR  = {Rudnicki, Piotr},
      TITLE   = {Representation Theorem for Free Continuous Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {185--188},
      NUMBER  = {{\bf 2}})

@ARTICLE(GRAPH_4.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Rudnicki, Piotr},
      TITLE   = {Oriented Chains},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {189--192},
      NUMBER  = {{\bf 2}})

@ARTICLE(JGRAPH_1.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Graph Theoretical Properties of Arcs in the Plane and {F}ashoda {M}eet {T}heorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {193--201},
      NUMBER  = {{\bf 2}})

@ARTICLE(IDEA_1.ABS,
      AUTHOR  = {Fuwa, Yasushi and Fujisawa, Yoshinori},
      TITLE   = {Algebraic Group on Fixed-length Bit Integer and its Adaptation to {IDEA} Cryptography},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {203--215},
      NUMBER  = {{\bf 2}})

@ARTICLE(TOPGRP_1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Definition and Basic Properties of Topological Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {217--225},
      NUMBER  = {{\bf 2}})

@ARTICLE(MSSUBLAT.ABS,
      AUTHOR  = {Naumowicz, Adam and Marasik, Agnieszka Julia},
      TITLE   = {The Correspondence Between Lattices of Subalgebras of  Universal Algebras and Many Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {227--231},
      NUMBER  = {{\bf 2}})

@ARTICLE(CONLAT_1.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {Introduction to Concept Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {233--241},
      NUMBER  = {{\bf 2}})

@ARTICLE(PARTIT1.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Jia, Kui},
      TITLE   = {A Theory of Partitions. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {243--247},
      NUMBER  = {{\bf 2}})

@ARTICLE(BVFUNC_1.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Jia, Kui},
      TITLE   = {A Theory of {B}oolean Valued Functions and Partitions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {249--254},
      NUMBER  = {{\bf 2}})

@ARTICLE(SIN_COS.ABS,
      AUTHOR  = {Yang, Yuguang and Shidama, Yasunari},
      TITLE   = {Trigonometric Functions and Existence of Circle Ratio},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {255--263},
      NUMBER  = {{\bf 2}})

@ARTICLE(SPRECT_3.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {Some Properties of Special Polygonal Curves},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {265--272},
      NUMBER  = {{\bf 2}})

@ARTICLE(VECTMETR.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Real Linear-Metric Space and Isometric Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {273--277},
      NUMBER  = {{\bf 2}})

@ARTICLE(YELLOW13.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Introduction to Meet-Continuous Topological Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {279--283},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL23.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Bases of Continuous Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {285--294},
      NUMBER  = {{\bf 2}})

@ARTICLE(SCMRING1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Construction of {\SCM} over Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {295--300},
      NUMBER  = {{\bf 2}})

@ARTICLE(SCMRING2.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Basic Properties of {\SCM} over Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {301--305},
      NUMBER  = {{\bf 2}})

@ARTICLE(BVFUNC_2.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Nakamura, Yatsuka},
      TITLE   = {A Theory of {B}oolean Valued Functions and Quantifiers with Respect to Partitions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {307--312},
      NUMBER  = {{\bf 2}})

@ARTICLE(BVFUNC_3.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Nakamura, Yatsuka},
      TITLE   = {Predicate Calculus for {B}oolean Valued Functions. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {313--315},
      NUMBER  = {{\bf 2}})

@ARTICLE(PEPIN.ABS,
      AUTHOR  = {Fujisawa, Yoshinori and Fuwa, Yasushi and Shimizu, Hidetaka},
      TITLE   = {Public-Key Cryptography and {P}epin's Test for the Primality of {F}ermat Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {317--321},
      NUMBER  = {{\bf 2}})

@ARTICLE(HEYTING2.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Lattice of Substitutions is a {H}eyting Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1998},
      VOLUME  = 7,
      PAGES   = {323--327},
      NUMBER  = {{\bf 2}})

@ARTICLE(JORDAN2C.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej and Byli\'nski, Czes{\l}aw},
      TITLE   = {Bounded Domains and Unbounded Domains},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {1--13},
      NUMBER  = {{\bf 1}})

@ARTICLE(REVROT_1.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Rotating and Reversing},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {15--20},
      NUMBER  = {{\bf 1}})

@ARTICLE(SPRECT_4.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {On the Components of the Complement of a Special Polygonal Curve},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {21--23},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN8.ABS,
      AUTHOR  = {Byli\'nski, Czes\l{}aw},
      TITLE   = {Gauges},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {25--27},
      NUMBER  = {{\bf 1}})

@ARTICLE(INT_3.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {The Ring of Integers, Euclidean Rings and Modulo Integers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {29--34},
      NUMBER  = {{\bf 1}})

@ARTICLE(GATE_1.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Logic Gates and Logical Equivalence of Adders},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {35--45},
      NUMBER  = {{\bf 1}})

@ARTICLE(FRECHET2.ABS,
      AUTHOR  = {Skorulski, Bart{\l}omiej},
      TITLE   = {The Sequential Closure Operator in Sequential and {F}rechet Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {47--54},
      NUMBER  = {{\bf 1}})

@ARTICLE(BORSUK_3.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Properties of the Product of Compact Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {55--59},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPREAL6.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Compactness of the Bounded Closed Subsets of ${\calE}^2_{\rmT}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {61--68},
      NUMBER  = {{\bf 1}})

@ARTICLE(HILBERT1.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {{H}ilbert Positive Propositional Calculus},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {69--72},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPREAL7.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Homeomorphism between [:${\calE}^i_{\rmT}, {\calE}^j_{\rmT}$:] and ${\calE}^{i+j}_{\rmT}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {73--76},
      NUMBER  = {{\bf 1}})

@ARTICLE(FSCIRC_1.ABS,
      AUTHOR  = {Wasaki, Katsumi and Endou, Noboru},
      TITLE   = {Full Subtracter Circuit. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {77--81},
      NUMBER  = {{\bf 1}})

@ARTICLE(GATE_2.ABS,
      AUTHOR  = {Yang, Yuguang and Wasaki, Katsumi and Fuwa, Yasushi and Nakamura, Yatsuka},
      TITLE   = {Correctness of Binary Counter Circuits},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {83--85},
      NUMBER  = {{\bf 1}})

@ARTICLE(GATE_3.ABS,
      AUTHOR  = {Yang, Yuguang and Wasaki, Katsumi and Fuwa, Yasushi and Nakamura, Yatsuka},
      TITLE   = {Correctness of {J}ohnson Counter Circuits},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {87--91},
      NUMBER  = {{\bf 1}})

@ARTICLE(INTEGRA1.ABS,
      AUTHOR  = {Endou, Noboru and Korni{\l}owicz, Artur},
      TITLE   = {The Definition of the {R}iemann Definite Integral and some Related Lemmas},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {93--102},
      NUMBER  = {{\bf 1}})

@ARTICLE(SIN_COS2.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Yang, Yuguang},
      TITLE   = {Properties of the Trigonometric Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {103--106},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC_4.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Nakamura, Yatsuka},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {107--109},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC_5.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Nakamura, Yatsuka},
      TITLE   = {Propositional Calculus for Boolean Valued Functions. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {111--113},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC_6.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Nakamura, Yatsuka},
      TITLE   = {Propositional Calculus for Boolean Valued Functions. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {115--117},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMISORT.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {Insert Sort on \SCMFSA},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {119--127},
      NUMBER  = {{\bf 1}})

@ARTICLE(GATE_4.ABS,
      AUTHOR  = {Yang, Yuguang and Wasaki, Katsumi and Fuwa, Yasushi and Nakamura, Yatsuka},
      TITLE   = {Correctness of a Cyclic Redundancy Check Code Generator},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {129--132},
      NUMBER  = {{\bf 1}})

@ARTICLE(HILBERT2.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Defining by Structural Induction in the Positive Propositional Language},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {133--137},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOBRD13.ABS,
      AUTHOR  = {Byli\'nski, Czes{\l}aw},
      TITLE   = {Some Properties of Cells on {G}o-Board},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {139--146},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC_7.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Propositional Calculus for Boolean Valued Functions. {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {147--148},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC_8.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Propositional Calculus for Boolean Valued Functions. {P}art {IV}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {149--150},
      NUMBER  = {{\bf 1}})

@ARTICLE(GENEALG1.ABS,
      AUTHOR  = {Uchibori, Akihiko and Endou, Noboru},
      TITLE   = {Basic Properties of Genetic Algorithm},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {151--160},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC_9.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Propositional Calculus for Boolean Valued Functions. {P}art {V}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {161--162},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOBRD14.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Properties of Left and Right Components},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {163--168},
      NUMBER  = {{\bf 1}})

@ARTICLE(LATTICE6.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {Noetherian Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {169--174},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMPDS_1.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {A Small Computer Model with Push-Down Stack},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {175--182},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMPDS_2.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {The {SCMPDS} Computer and the Basic Semantics of its Instructions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {183--191},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMPDS_3.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {Computation and Program Shift in the {SCMPDS} Computer},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {193--199},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMPDS_4.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {The Construction and Shiftability of Program Blocks for {SCMPDS}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {201--210},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMPDS_5.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {Computation of Two Consecutive Program Blocks for {SCMPDS}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {211--217},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMPDS_6.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {The Construction and Computation of Conditional Statements for {SCMPDS}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {1999},
      VOLUME  = 8,
      PAGES   = {219--234},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMP_GCD.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {Recursive {E}uclide Algorithm},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {1--4},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL24.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {{S}cott-Continuous Functions. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {5--11},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW14.ABS,
      AUTHOR  = {Gryko, Jaros{\l}aw and Korni{\l}owicz, Artur},
      TITLE   = {Some Properties of Isomorphism between Relational Structures. {O}n the Product of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {13--18},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN9.ABS,
      AUTHOR  = {Byli\'nski, Czes{\l}aw and \.Zynel, Mariusz},
      TITLE   = {Cages -- the External Approximation of {J}ordan's Curve},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {19--24},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW15.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Components and Basis of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {25--29},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN10.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Properties of the External Approximation of {J}ordan's Curve},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {31--34},
      NUMBER  = {{\bf 1}})

@ARTICLE(IRRAT_1.ABS,
      AUTHOR  = {Wiedijk, Freek},
      TITLE   = {Irrationality of $e$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {35--39},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL25.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Gryko, Jaros{\l}aw},
      TITLE   = {Injective Spaces. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {41--47},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC10.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Propositional Calculus for Boolean Valued Functions. {P}art {VI}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {49--50},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC11.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Nakamura, Yatsuka},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {51--53},
      NUMBER  = {{\bf 1}})

@ARTICLE(CONLAT_2.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {A Characterization of Concept Lattices. {D}ual Concept Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {55--59},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC12.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Nakamura, Yatsuka},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {IV}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {61--63},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC13.ABS,
      AUTHOR  = {Kobayashi, Shunichi and Nakamura, Yatsuka},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {V}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {65--70},
      NUMBER  = {{\bf 1}})

@ARTICLE(RADIX_1.ABS,
      AUTHOR  = {Fujisawa, Yoshinori and Fuwa, Yasushi},
      TITLE   = {Definitions of Radix-$2^k$ Signed-Digit Number and its Adder Algorithm},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {71--75},
      NUMBER  = {{\bf 1}})

@ARTICLE(YELLOW16.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Retracts and Inheritance},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {77--85},
      NUMBER  = {{\bf 1}})

@ARTICLE(ALGSPEC1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Technical Preliminaries to Algebraic Specifications},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {87--93},
      NUMBER  = {{\bf 1}})

@ARTICLE(POLYNOM1.ABS,
      AUTHOR  = {Rudnicki, Piotr and Trybulec, Andrzej},
      TITLE   = {Multivariate Polynomials  with Arbitrary Number of Variables},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {95--110},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL26.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Continuous Lattices of Maps between {T}$_0$ Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {111--117},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC14.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {VI}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {119--121},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC15.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {VII}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {123--125},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC16.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {VIII}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {127--129},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC17.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {IX}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {131--133},
      NUMBER  = {{\bf 1}})

@ARTICLE(ASYMPT_0.ABS,
      AUTHOR  = {Krueger, Richard and Rudnicki, Piotr and Shelley, Paul},
      TITLE   = {Asymptotic Notation. {P}art {I}: {T}heory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {135--142},
      NUMBER  = {{\bf 1}})

@ARTICLE(ASYMPT_1.ABS,
      AUTHOR  = {Krueger, Richard and Rudnicki, Piotr and Shelley, Paul},
      TITLE   = {Asymptotic Notation. {P}art {II}: {E}xamples and Problems},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {143--154},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC18.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {X}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {155--156},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC19.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {XI}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {157--159},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC20.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Four Variable Predicate Calculus for Boolean Valued Functions. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {161--165},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC21.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Four Variable Predicate Calculus for Boolean Valued Functions. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {167--170},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL27.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Naumowicz, Adam},
      TITLE   = {Function Spaces in the Category of Directed Suprema Preserving Maps},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {171--177},
      NUMBER  = {{\bf 1}})

@ARTICLE(CFUNCT_1.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Property of Complex Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {179--184},
      NUMBER  = {{\bf 1}})

@ARTICLE(CFCONT_1.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Property of Complex Sequence and Continuity of Complex Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {185--190},
      NUMBER  = {{\bf 1}})

@ARTICLE(INTEGRA2.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Scalar Multiple of {R}iemann Definite Integral},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {191--196},
      NUMBER  = {{\bf 1}})

@ARTICLE(INTEGRA3.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {{D}arboux's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {197--200},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC22.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Five Variable Predicate Calculus for Boolean Valued Functions. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {201--204},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC23.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Six Variable Predicate Calculus for Boolean Valued Functions. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {205--208},
      NUMBER  = {{\bf 1}})

@ARTICLE(SCMPDS_7.ABS,
      AUTHOR  = {Chen, Jing-Chao and Rudnicki, Piotr},
      TITLE   = {The Construction and Computation of for-loop Programs for {SCMPDS}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {209--219},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC24.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Predicate Calculus for Boolean Valued Functions. {P}art {XII}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {221--235},
      NUMBER  = {{\bf 1}})

@ARTICLE(WAYBEL28.ABS,
      AUTHOR  = {Skorulski, Bart{\l}omiej},
      TITLE   = {Lim-Inf Convergence},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {237--240},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL29.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Naumowicz, Adam},
      TITLE   = {The Characterization of the Continuity of Topologies},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {241--247},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL30.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Meet Continuous Lattices Revisited},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {249--254},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL31.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Weights of Continuous Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {255--259},
      NUMBER  = {{\bf 2}})

@ARTICLE(LATTICE7.ABS,
      AUTHOR  = {Dudzicz, Marek},
      TITLE   = {Representation Theorem for Finite Distributive Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {261--264},
      NUMBER  = {{\bf 2}})

@ARTICLE(COMPLFLD.ABS,
      AUTHOR  = {Milewska, Anna Justyna},
      TITLE   = {The Field of Complex Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {265--269},
      NUMBER  = {{\bf 2}})

@ARTICLE(INTEGRA4.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Integrability of Bounded Total Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {271--274},
      NUMBER  = {{\bf 2}})

@ARTICLE(RADIX_2.ABS,
      AUTHOR  = {Fuwa, Yasushi and Fujisawa, Yoshinori},
      TITLE   = {High-Speed Algorithms for {RSA} Cryptograms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {275--279},
      NUMBER  = {{\bf 2}})

@ARTICLE(INTEGRA5.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Definition of Integrability for Partial Functions from ${\BbbR}$ to ${\BbbR}$ and Integrability for Continuous Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {281--284},
      NUMBER  = {{\bf 2}})

@ARTICLE(RFUNCT_4.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Introduction to Several Concepts of Convexity and Semicontinuity for Function from ${\BbbR}$ to ${\BbbR}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {285--289},
      NUMBER  = {{\bf 2}})

@ARTICLE(AMISTD_1.ABS,
      AUTHOR  = {Trybulec, Andrzej and Rudnicki, Piotr and Korni{\l}owicz, Artur},
      TITLE   = {Standard Ordering of Instruction Locations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {291--301},
      NUMBER  = {{\bf 2}})

@ARTICLE(AMISTD_2.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Composition of Macro Instructions of Standard Computers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {303--316},
      NUMBER  = {{\bf 2}})

@ARTICLE(SCMRING3.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Properties of Instructions of {SCM} over Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {317--322},
      NUMBER  = {{\bf 2}})

@ARTICLE(CARD_FIL.ABS,
      AUTHOR  = {Urban, Josef},
      TITLE   = {Basic Facts about Inaccessible and Measurable Cardinals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {323--329},
      NUMBER  = {{\bf 2}})

@ARTICLE(POLYNOM2.ABS,
      AUTHOR  = {Schwarzweller, Christoph and Trybulec, Andrzej},
      TITLE   = {The Evaluation of Multivariate Polynomials},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {331--338},
      NUMBER  = {{\bf 2}})

@ARTICLE(POLYNOM3.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {The Ring of Polynomials},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {339--346},
      NUMBER  = {{\bf 2}})

@ARTICLE(POLYEQ_1.ABS,
      AUTHOR  = {Liang, Xiquan},
      TITLE   = {Solving Roots of Polynomial Equations of Degree 2 and 3 with Real Coefficients},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {347--350},
      NUMBER  = {{\bf 2}})

@ARTICLE(FUZZY_1.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {The Concept of Fuzzy Set and Membership Function and Basic Properties of Fuzzy Set Operation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {351--356},
      NUMBER  = {{\bf 2}})

@ARTICLE(FUZZY_2.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Basic Properties of Fuzzy Set Operation and Membership Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {357--362},
      NUMBER  = {{\bf 2}})

@ARTICLE(HAHNBAN1.ABS,
      AUTHOR  = {Milewska, Anna Justyna},
      TITLE   = {The {H}ahn {B}anach Theorem in the Vector Space over the Field of Complex Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {363--371},
      NUMBER  = {{\bf 2}})

@ARTICLE(YELLOW17.ABS,
      AUTHOR  = {Skorulski, Bart{\l}omiej},
      TITLE   = {The {T}ichonov {T}heorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {373--376},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL32.ABS,
      AUTHOR  = {Gr\k{a}dzka, Ewa},
      TITLE   = {On the Order-consistent Topology of Complete and Uncomplete Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {377--382},
      NUMBER  = {{\bf 2}})

@ARTICLE(PENCIL_1.ABS,
      AUTHOR  = {Naumowicz, Adam},
      TITLE   = {On {S}egre's Product of Partial Line Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {383--390},
      NUMBER  = {{\bf 2}})

@ARTICLE(POLYNOM4.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {The Evaluation of Polynomials},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {391--395},
      NUMBER  = {{\bf 2}})

@ARTICLE(SCMPDS_8.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {The Construction and Computation of While-Loop Programs for {SCMPDS}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {397--405},
      NUMBER  = {{\bf 2}})

@ARTICLE(SCPISORT.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {Insert Sort on {SCMPDS}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {407--412},
      NUMBER  = {{\bf 2}})

@ARTICLE(SCPQSORT.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {Quick Sort on {SCMPDS}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {413--418},
      NUMBER  = {{\bf 2}})

@ARTICLE(SCPINVAR.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {Justifying the Correctness of the {F}ibonacci Sequence and the {E}uclide Algorithm by Loop-Invariant},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {419--427},
      NUMBER  = {{\bf 2}})

@ARTICLE(ORDERS_4.ABS,
      AUTHOR  = {Pruszy\'nska, Marta and Dudzicz, Marek},
      TITLE   = {On the Isomorphism between Finite Chains},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {429--430},
      NUMBER  = {{\bf 2}})

@ARTICLE(LATTICE8.ABS,
      AUTHOR  = {{\L}api\'nski, Mariusz},
      TITLE   = {The {J}\'onsson {T}heorem about the Representation of Modular Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {431--438},
      NUMBER  = {{\bf 2}})

@ARTICLE(HILBERT3.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {The Canonical Formulae},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {441--447},
      NUMBER  = {{\bf 3}})

@ARTICLE(HEYTING3.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {The Incompleteness of the Lattice of Substitutions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {449--454},
      NUMBER  = {{\bf 3}})

@ARTICLE(COMPTRIG.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Trigonometric Form of Complex Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {455--460},
      NUMBER  = {{\bf 3}})

@ARTICLE(POLYNOM5.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Fundamental Theorem of Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {461--470},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINSEQ_7.ABS,
      AUTHOR  = {Yamazaki, Hiroshi and Fujisawa, Yoshinori and Nakamura, Yatsuka},
      TITLE   = {On Replace Function and Swap Function for Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {471--474},
      NUMBER  = {{\bf 3}})

@ARTICLE(GATE_5.ABS,
      AUTHOR  = {Yamazaki, Hiroshi and Wasaki, Katsumi},
      TITLE   = {The Correctness of the High Speed Array Multiplier Circuits},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {475--479},
      NUMBER  = {{\bf 3}})

@ARTICLE(JCT_MISC.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Some Lemmas for the {J}ordan Curve Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {481--484},
      NUMBER  = {{\bf 3}})

@ARTICLE(CARD_LAR.ABS,
      AUTHOR  = {Urban, Josef},
      TITLE   = {Mahlo and Inaccessible Cardinals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {485--489},
      NUMBER  = {{\bf 3}})

@ARTICLE(EXTREAL1.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Basic Properties of Extended Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {491--494},
      NUMBER  = {{\bf 3}})

@ARTICLE(MESFUNC1.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Definitions and Basic Properties of Measurable Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {495--500},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN1A.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Milewski, Robert and Naumowicz, Adam and Trybulec, Andrzej},
      TITLE   = {Gauges and Cages. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {501--509},
      NUMBER  = {{\bf 3}})

@ARTICLE(EXTREAL2.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Some Properties of Extended Real Numbers Operations: abs, min and max},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {511--516},
      NUMBER  = {{\bf 3}})

@ARTICLE(FUZZY_3.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {The Concept of Fuzzy Relation and Basic Properties of its Operation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {517--524},
      NUMBER  = {{\bf 3}})

@ARTICLE(MESFUNC2.ABS,
      AUTHOR  = {Endou, Noboru and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {The Measurability of Extended Real Valued Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {525--529},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN1B.ABS,
      AUTHOR  = {Milewski, Robert and Trybulec, Andrzej and Korni{\l}owicz, Artur and Naumowicz, Adam},
      TITLE   = {Some Properties of Cells and Arcs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {531--535},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINTOPO2.ABS,
      AUTHOR  = {Liu, Gang and Fuwa, Yasushi and Eguchi, Masayoshi},
      TITLE   = {Formal Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {537--543},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN1C.ABS,
      AUTHOR  = {Grabowski, Adam and Korni{\l}owicz, Artur and Trybulec, Andrzej},
      TITLE   = {Some Properties of Cells and Gauges},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {545--548},
      NUMBER  = {{\bf 3}})

@ARTICLE(SPRECT_5.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {Again on the Order on a Special Polygon},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {549--553},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN1D.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Milewski, Robert},
      TITLE   = {Gauges and Cages. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {555--558},
      NUMBER  = {{\bf 3}})

@ARTICLE(BINOM.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {The Binomial Theorem for Algebraic Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {559--564},
      NUMBER  = {{\bf 3}})

@ARTICLE(IDEAL_1.ABS,
      AUTHOR  = {Backer, Jonathan and Rudnicki, Piotr and Schwarzweller, Christoph},
      TITLE   = {Ring Ideals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {565--582},
      NUMBER  = {{\bf 3}})

@ARTICLE(HILBASIS.ABS,
      AUTHOR  = {Backer, Jonathan and Rudnicki, Piotr},
      TITLE   = {Hilbert Basis Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {583--589},
      NUMBER  = {{\bf 3}})

@ARTICLE(DYNKIN.ABS,
      AUTHOR  = {Merkl, Franz},
      TITLE   = {Dynkin's Lemma in Measure Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {591--595},
      NUMBER  = {{\bf 3}})

@ARTICLE(TAXONOM1.ABS,
      AUTHOR  = {Giero, Mariusz and Matuszewski, Roman},
      TITLE   = {Lower Tolerance. {P}reliminaries to {W}roclaw Taxonomy},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {597--603},
      NUMBER  = {{\bf 3}})

@ARTICLE(YELLOW18.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Concrete Categories},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {605--621},
      NUMBER  = {{\bf 3}})

@ARTICLE(PARTIT_2.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Classes of Independent Partitions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {623--625},
      NUMBER  = {{\bf 3}})

@ARTICLE(URYSOHN2.ABS,
      AUTHOR  = {Bia{\l}as, J\'ozef and Nakamura, Yatsuka},
      TITLE   = {Some Properties of Dyadic Numbers and Intervals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {627--630},
      NUMBER  = {{\bf 3}})

@ARTICLE(URYSOHN3.ABS,
      AUTHOR  = {Bia{\l}as, J\'ozef and Nakamura, Yatsuka},
      TITLE   = {The {U}rysohn Lemma},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {631--636},
      NUMBER  = {{\bf 3}})

@ARTICLE(POLYALG1.ABS,
      AUTHOR  = {Gr\k{a}dzka, Ewa},
      TITLE   = {The Algebra of Polynomials},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {637--643},
      NUMBER  = {{\bf 3}})

@ARTICLE(CIRCTRM1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Circuit Generated by Terms and Circuit Calculating Terms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {645--657},
      NUMBER  = {{\bf 3}})

@ARTICLE(AMI_6.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Instructions of \SCM},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {659--663},
      NUMBER  = {{\bf 4}})

@ARTICLE(AMI_7.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Input and Output of Instructions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {665--671},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMFSA10.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Instructions of \SCMFSA},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {673--679},
      NUMBER  = {{\bf 4}})

@ARTICLE(ROBBINS1.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Robbins Algebras vs. {B}oolean Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {681--690},
      NUMBER  = {{\bf 4}})

@ARTICLE(FUZZY_4.ABS,
      AUTHOR  = {Endou, Noboru and Mitsuishi, Takashi and Ohkubo, Keiji},
      TITLE   = {Properties of Fuzzy Relation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {691--695},
      NUMBER  = {{\bf 4}})

@ARTICLE(JGRAPH_2.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {On {O}utside {F}ashoda {M}eet {T}heorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {697--704},
      NUMBER  = {{\bf 4}})

@ARTICLE(COMPUT_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Rudnicki, Piotr},
      TITLE   = {The Set of Primitive Recursive Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {705--720},
      NUMBER  = {{\bf 4}})

@ARTICLE(TURING_1.ABS,
      AUTHOR  = {Chen, Jing-Chao and Nakamura, Yatsuka},
      TITLE   = {Introduction to {T}uring Machines},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {721--732},
      NUMBER  = {{\bf 4}})

@ARTICLE(YELLOW19.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Endou, Noboru and Sakai, Yuji},
      TITLE   = {On the Characterizations of Compactness},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {733--738},
      NUMBER  = {{\bf 4}})

@ARTICLE(WAYBEL33.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Endou, Noboru},
      TITLE   = {Compactness of Lim-inf Topology},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {739--743},
      NUMBER  = {{\bf 4}})

@ARTICLE(YELLOW20.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Miscellaneous Facts about Functors},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {745--754},
      NUMBER  = {{\bf 4}})

@ARTICLE(YELLOW21.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Categorial Background for Duality Theory},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {755--765},
      NUMBER  = {{\bf 4}})

@ARTICLE(WAYBEL34.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Duality Based on the {G}alois Connection. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {767--778},
      NUMBER  = {{\bf 4}})

@ARTICLE(MSAFREE3.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Korni{\l}owicz, Artur},
      TITLE   = {Yet Another Construction of Free Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {779--785},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN1E.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Upper and Lower Sequence of a Cage},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {787--790},
      NUMBER  = {{\bf 4}})

@ARTICLE(POLYNOM6.ABS,
      AUTHOR  = {Dzienis, Barbara},
      TITLE   = {On Polynomials with Coefficients in a Ring of Polynomials},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {791--794},
      NUMBER  = {{\bf 4}})

@ARTICLE(PENCIL_2.ABS,
      AUTHOR  = {Naumowicz, Adam},
      TITLE   = {On Cosets in {S}egre's Product of Partial Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {795--800},
      NUMBER  = {{\bf 4}})

@ARTICLE(JGRAPH_3.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {On the Simple Closed Curve Property of the Circle and the {F}ashoda {M}eet {T}heorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {801--808},
      NUMBER  = {{\bf 4}})

@ARTICLE(PYTHTRIP.ABS,
      AUTHOR  = {Wiedijk, Freek},
      TITLE   = {Pythagorean Triples},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {809--812},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN1F.ABS,
      AUTHOR  = {Naumowicz, Adam},
      TITLE   = {Some Remarks on Finite Sequences on Go-boards},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {813--816},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN1G.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Upper and Lower Sequence on the Cage. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {817--823},
      NUMBER  = {{\bf 4}})

@ARTICLE(AFINSQ_1.ABS,
      AUTHOR  = {Tsunetou, Tetsuya and Bancerek, Grzegorz and Nakamura, Yatsuka},
      TITLE   = {Zero-Based Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {825--829},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN1H.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {More on the External Approximation of a~Continuum},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {831--841},
      NUMBER  = {{\bf 4}})

@ARTICLE(TOPREAL8.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {More on the Finite Sequences on the Plane},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {843--847},
      NUMBER  = {{\bf 4}})

@ARTICLE(POLYNOM7.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {More on Multivariate Polynomials: Monomials and Constant Polynomials},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {849--855},
      NUMBER  = {{\bf 4}})

@ARTICLE(FSM_2.ABS,
      AUTHOR  = {Kunimune, Hisayoshi and Bancerek, Grzegorz and Nakamura, Yatsuka},
      TITLE   = {On State Machines of Calculating Type},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {857--864},
      NUMBER  = {{\bf 4}})

@ARTICLE(TAXONOM2.ABS,
      AUTHOR  = {Giero, Mariusz},
      TITLE   = {Hierarchies and Classifications of Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2001},
      VOLUME  = 9,
      PAGES   = {865--869},
      NUMBER  = {{\bf 4}})

@ARTICLE(JGRAPH_4.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Fan Homeomorphisms in the Plane},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {1--19},
      NUMBER  = {{\bf 1}})

@ARTICLE(RCOMP_2.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Half Open Intervals in Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {21--22},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN1I.ABS,
      AUTHOR  = {Naumowicz, Adam and Milewski, Robert},
      TITLE   = {Some Remarks on Clockwise Oriented Sequences on Go-boards},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {23--27},
      NUMBER  = {{\bf 1}})

@ARTICLE(DICKSON.ABS,
      AUTHOR  = {Lee, Gilbert and Rudnicki, Piotr},
      TITLE   = {Dickson's Lemma},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {29--37},
      NUMBER  = {{\bf 1}})

@ARTICLE(BAGORDER.ABS,
      AUTHOR  = {Lee, Gilbert and Rudnicki, Piotr},
      TITLE   = {On Ordering of Bags},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {39--46},
      NUMBER  = {{\bf 1}})

@ARTICLE(CIRCCMB2.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Yamaguchi, Shin'nosuke and Shidama, Yasunari},
      TITLE   = {Combining of Multi Cell Circuits},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {47--64},
      NUMBER  = {{\bf 1}})

@ARTICLE(FACIRC_2.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Yamaguchi, Shin'nosuke and Wasaki, Katsumi},
      TITLE   = {Full Adder Circuit. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {65--71},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN1J.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Upper and Lower Sequence on the Cage, Upper and Lower Arcs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {73--80},
      NUMBER  = {{\bf 2}})

@ARTICLE(FIB_NUM.ABS,
      AUTHOR  = {Solovay, Robert M.},
      TITLE   = {Fibonacci Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {81--83},
      NUMBER  = {{\bf 2}})

@ARTICLE(JORDAN11.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Preparing the Internal Approximations of Simple Closed Curves},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {85--87},
      NUMBER  = {{\bf 2}})

@ARTICLE(JORDAN12.ABS,
      AUTHOR  = {Giero, Mariusz},
      TITLE   = {On the General Position of Special Polygons},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {89--95},
      NUMBER  = {{\bf 2}})

@ARTICLE(JORDAN13.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {Introducing Spans},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {97--98},
      NUMBER  = {{\bf 2}})

@ARTICLE(JGRAPH_5.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {General {F}ashoda {M}eet {T}heorem for Unit Circle},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {99--109},
      NUMBER  = {{\bf 2}})

@ARTICLE(JORDAN14.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Properties of the Internal Approximation of {J}ordan's Curve},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {111--115},
      NUMBER  = {{\bf 2}})

@ARTICLE(CIRCCMB3.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Naumowicz, Adam},
      TITLE   = {Preliminaries to Automatic Generation  of {M}izar Documentation for Circuits},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {117--133},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN15.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Properties of the Upper and Lower Sequence on the Cage},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {135--143},
      NUMBER  = {{\bf 3}})

@ARTICLE(BORSUK_4.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {On the Decompositions of Intervals  and Simple Closed Curves},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {145--151},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN1K.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {On the Minimal Distance Between Sets  in {E}uclidean Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {153--158},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPMETR3.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {Sequences of Metric Spaces and  an Abstract Intermediate Value Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {159--161},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN16.ABS,
      AUTHOR  = {Trybulec, Andrzej and Nakamura, Yatsuka},
      TITLE   = {On the Decomposition of a Simple Closed Curve into Two Arcs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {163--167},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN17.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Ordering of Points on a Curve.  {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {169--171},
      NUMBER  = {{\bf 3}})

@ARTICLE(JORDAN18.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Ordering of Points on a Curve.  {P}art {IV}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {173--177},
      NUMBER  = {{\bf 3}})

@ARTICLE(OSALG_1.ABS,
      AUTHOR  = {Urban, Josef},
      TITLE   = {Order Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {179--188},
      NUMBER  = {{\bf 3}})

@ARTICLE(OSALG_2.ABS,
      AUTHOR  = {Urban, Josef},
      TITLE   = {Subalgebras of an Order Sorted Algebra. {L}attice of Subalgebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {189--196},
      NUMBER  = {{\bf 3}})

@ARTICLE(OSALG_3.ABS,
      AUTHOR  = {Urban, Josef},
      TITLE   = {Homomorphisms of Order Sorted Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {197--200},
      NUMBER  = {{\bf 3}})

@ARTICLE(OSALG_4.ABS,
      AUTHOR  = {Urban, Josef},
      TITLE   = {Order Sorted Quotient Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {201--210},
      NUMBER  = {{\bf 3}})

@ARTICLE(OSAFREE.ABS,
      AUTHOR  = {Urban, Josef},
      TITLE   = {Free Order Sorted Universal Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2002},
      VOLUME  = 10,
      PAGES   = {211--225},
      NUMBER  = {{\bf 3}})

@ARTICLE(RUSUB_1.ABS,
      AUTHOR  = {Endou, Noboru and Mitsuishi, Takashi and Shidama, Yasunari},
      TITLE   = {Subspaces and Cosets of Subspace of Real Unitary Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {1--7},
      NUMBER  = {{\bf 1}})

@ARTICLE(RUSUB_2.ABS,
      AUTHOR  = {Endou, Noboru and Mitsuishi, Takashi and Shidama, Yasunari},
      TITLE   = {Operations on Subspaces in Real Unitary Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {9--16},
      NUMBER  = {{\bf 1}})

@ARTICLE(RUSUB_3.ABS,
      AUTHOR  = {Endou, Noboru and Mitsuishi, Takashi and Shidama, Yasunari},
      TITLE   = {Linear Combinations in Real Unitary Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {17--22},
      NUMBER  = {{\bf 1}})

@ARTICLE(RUSUB_4.ABS,
      AUTHOR  = {Endou, Noboru and Mitsuishi, Takashi and Shidama, Yasunari},
      TITLE   = {Dimension of Real Unitary Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {23--28},
      NUMBER  = {{\bf 1}})

@ARTICLE(SIN_COS3.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Endou, Noboru and Ohkubo, Keiji},
      TITLE   = {Trigonometric Functions on Complex Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {29--32},
      NUMBER  = {{\bf 1}})

@ARTICLE(RUSUB_5.ABS,
      AUTHOR  = {Endou, Noboru and Mitsuishi, Takashi and Shidama, Yasunari},
      TITLE   = {Topology of Real Unitary Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {33--38},
      NUMBER  = {{\bf 1}})

@ARTICLE(ARMSTRNG.ABS,
      AUTHOR  = {Armstrong, William W. and Nakamura, Yatsuka and Rudnicki, Piotr},
      TITLE   = {Armstrong's Axioms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {39--51},
      NUMBER  = {{\bf 1}})

@ARTICLE(CONVEX1.ABS,
      AUTHOR  = {Endou, Noboru and Mitsuishi, Takashi and Shidama, Yasunari},
      TITLE   = {Convex Sets and Convex Combinations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {53--58},
      NUMBER  = {{\bf 1}})

@ARTICLE(VECTSP10.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Quotient Vector Spaces and Functionals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {59--68},
      NUMBER  = {{\bf 1}})

@ARTICLE(BILINEAR.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Bilinear Functionals in Vector Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {69--86},
      NUMBER  = {{\bf 1}})

@ARTICLE(HERMITAN.ABS,
      AUTHOR  = {Kotowicz, Jaros{\l}aw},
      TITLE   = {Hermitan Functionals. {C}anonical Construction of Scalar Product in Quotient Vector Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {87--98},
      NUMBER  = {{\bf 1}})

@ARTICLE(NECKLACE.ABS,
      AUTHOR  = {Retel, Krzysztof},
      TITLE   = {The Class of Series -- Parallel Graphs. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {99--103},
      NUMBER  = {{\bf 1}})

@ARTICLE(TERMORD.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {Term Orders},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {105--111},
      NUMBER  = {{\bf 1}})

@ARTICLE(POLYRED.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {Polynomial Reduction},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {113--123},
      NUMBER  = {{\bf 1}})

@ARTICLE(PNPROC_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Aoki, Mitsuru and Matsumoto, Akio and Shidama, Yasunari},
      TITLE   = {Processes in {P}etri nets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {125--132},
      NUMBER  = {{\bf 1}})

@ARTICLE(RADIX_3.ABS,
      AUTHOR  = {Niimura, Masaaki and Fuwa, Yasushi},
      TITLE   = {Improvement of Radix-$2^k$ Signed-Digit Number for High Speed Circuit},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {133--137},
      NUMBER  = {{\bf 2}})

@ARTICLE(RADIX_4.ABS,
      AUTHOR  = {Niimura, Masaaki and Fuwa, Yasushi},
      TITLE   = {High Speed Adder Algorithm with Radix-$2^k$ Sub Signed-Digit Number},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {139--141},
      NUMBER  = {{\bf 2}})

@ARTICLE(GRAPH_5.ABS,
      AUTHOR  = {Chen, Jing-Chao and Nakamura, Yatsuka},
      TITLE   = {The Underlying Principle of {D}ijkstra's Shortest Path Algorithm},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {143--152},
      NUMBER  = {{\bf 2}})

@ARTICLE(HAUSDORF.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {On the {H}ausdorff Distance Between Compact Subsets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {153--157},
      NUMBER  = {{\bf 2}})

@ARTICLE(CHAIN_1.ABS,
      AUTHOR  = {Wiedijk, Freek},
      TITLE   = {Chains on a Grating in {E}uclidean Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {159--167},
      NUMBER  = {{\bf 2}})

@ARTICLE(BHSP_5.ABS,
      AUTHOR  = {Yamazaki, Hiroshi and Shidama, Yasunari and Nakamura, Yatsuka},
      TITLE   = {Bessel's Inequality},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {169--173},
      NUMBER  = {{\bf 2}})

@ARTICLE(BINARI_4.ABS,
      AUTHOR  = {Kunimune, Hisayoshi and Nakamura, Yatsuka},
      TITLE   = {A Representation of Integers by Binary Arithmetics and Addition of Integers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {175--178},
      NUMBER  = {{\bf 2}})

@ARTICLE(EUCLID_2.ABS,
      AUTHOR  = {, Kanchun and Nakamura, Yatsuka},
      TITLE   = {The Inner Product of Finite Sequences  and of Points of $n$-dimensional Topological Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {179--183},
      NUMBER  = {{\bf 2}})

@ARTICLE(POLYEQ_2.ABS,
      AUTHOR  = {Liang, Xiquan},
      TITLE   = {Solving Roots of Polynomial Equation  of Degree 4 with Real Coefficients},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {185--187},
      NUMBER  = {{\bf 2}})

@ARTICLE(WAYBEL35.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Morphisms Into Chains. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {189--195},
      NUMBER  = {{\bf 2}})

@ARTICLE(BVFUNC25.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Propositional Calculus for {B}oolean Valued Functions. {P}art {VII}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {197--199},
      NUMBER  = {{\bf 2}})

@ARTICLE(OPOSET_1.ABS,
      AUTHOR  = {Moschner, Markus},
      TITLE   = {Basic Notions and Properties of Orthoposets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {201--210},
      NUMBER  = {{\bf 2}})

@ARTICLE(JGRAPH_6.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {General {F}ashoda Meet Theorem for Unit Circle and Square},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {213--224},
      NUMBER  = {{\bf 3}})

@ARTICLE(BHSP_6.ABS,
      AUTHOR  = {Yamazaki, Hiroshi and Suzuki, Yasumasa and Inou\'e, Takao and Shidama, Yasunari},
      TITLE   = {On Some Properties of Real {H}ilbert Space. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {225--229},
      NUMBER  = {{\bf 3}})

@ARTICLE(FSCIRC_2.ABS,
      AUTHOR  = {Yamaguchi, Shin'nosuke and Bancerek, Grzegorz and Wasaki, Katsumi},
      TITLE   = {Full Subtracter Circuit. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {231--236},
      NUMBER  = {{\bf 3}})

@ARTICLE(GRAPHSP.ABS,
      AUTHOR  = {Chen, Jing-Chao},
      TITLE   = {Dijkstra's Shortest Path Algorithm},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {237--247},
      NUMBER  = {{\bf 3}})

@ARTICLE(RSSPACE.ABS,
      AUTHOR  = {Endou, Noboru and Suzuki, Yasumasa and Shidama, Yasunari},
      TITLE   = {Real Linear Space of Real Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {249--253},
      NUMBER  = {{\bf 3}})

@ARTICLE(RSSPACE2.ABS,
      AUTHOR  = {Endou, Noboru and Suzuki, Yasumasa and Shidama, Yasunari},
      TITLE   = {Hilbert Space of Real Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {255--257},
      NUMBER  = {{\bf 3}})

@ARTICLE(INTPRO_1.ABS,
      AUTHOR  = {Inou\'e, Takao},
      TITLE   = {Intuitionistic Propositional Calculus in the Extended Framework with Modal Operator. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {259--266},
      NUMBER  = {{\bf 3}})

@ARTICLE(CONVEX2.ABS,
      AUTHOR  = {Endou, Noboru and Suzuki, Yasumasa and Shidama, Yasunari},
      TITLE   = {Some Properties for Convex Combinations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {267--270},
      NUMBER  = {{\bf 3}})

@ARTICLE(BHSP_7.ABS,
      AUTHOR  = {Yamazaki, Hiroshi and Suzuki, Yasumasa and Inou\'{e}, Takao and Shidama, Yasunari},
      TITLE   = {On Some Properties of Real {H}ilbert Space. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {271--273},
      NUMBER  = {{\bf 3}})

@ARTICLE(COMPLEX2.ABS,
      AUTHOR  = {Chang, Wenpai and Nakamura, Yatsuka and Rudnicki, Piotr},
      TITLE   = {Inner Products and Angles of Complex Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {275--280},
      NUMBER  = {{\bf 3}})

@ARTICLE(EUCLID_3.ABS,
      AUTHOR  = {Kubo, Akihiro and Nakamura, Yatsuka},
      TITLE   = {Angle and Triangle in {E}uclidian Topological Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {281--287},
      NUMBER  = {{\bf 3}})

@ARTICLE(NECKLA_2.ABS,
      AUTHOR  = {Retel, Krzysztof},
      TITLE   = {The Class of Series-Parallel Graphs.  {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {289--291},
      NUMBER  = {{\bf 3}})

@ARTICLE(GROEB_1.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {Characterization and Existence of {G}r\"{o}bner Bases},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {293--301},
      NUMBER  = {{\bf 3}})

@ARTICLE(GROEB_2.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {Construction of {G}r\"{o}bner bases.  {S}-Polynomials and Standard Representations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {303--312},
      NUMBER  = {{\bf 3}})

@ARTICLE(BORSUK_5.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {On the Subcontinua of a Real Line},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {313--322},
      NUMBER  = {{\bf 3}})

@ARTICLE(KURATO_1.ABS,
      AUTHOR  = {Bagi\'nska, Lilla Krystyna and Grabowski, Adam},
      TITLE   = {On the {K}uratowski Closure-Complement Problem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {323--329},
      NUMBER  = {{\bf 3}})

@ARTICLE(CONVEX3.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Convex Hull, Set of Convex Combinations and Convex Cone},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {331--333},
      NUMBER  = {{\bf 3}})

@ARTICLE(ROBBINS2.ABS,
      AUTHOR  = {Truszkowska, Wioletta and Grabowski, Adam},
      TITLE   = {On the Two Short Axiomatizations of Ortholattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {335--340},
      NUMBER  = {{\bf 3}})

@ARTICLE(MEMBERED.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {On the Sets Inhabited by Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {341--347},
      NUMBER  = {{\bf 4}})

@ARTICLE(CONVFUN1.ABS,
      AUTHOR  = {Ivanov, Grigory E.},
      TITLE   = {Definition of Convex Function  and {J}ensen's Inequality},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {349--354},
      NUMBER  = {{\bf 4}})

@ARTICLE(ABCMIZ_0.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {On Semilattice Structure of {M}izar Types},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {355--369},
      NUMBER  = {{\bf 4}})

@ARTICLE(EUCLID_4.ABS,
      AUTHOR  = {Kubo, Akihiro},
      TITLE   = {Lines in $n$-Dimensional {E}uclidean Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {371--376},
      NUMBER  = {{\bf 4}})

@ARTICLE(RSSPACE3.ABS,
      AUTHOR  = {Suzuki, Yasumasa and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Banach Space of Absolute Summable  Real Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {377--380},
      NUMBER  = {{\bf 4}})

@ARTICLE(EUCLID_5.ABS,
      AUTHOR  = {, Kanchun and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {Cross Products and Tripple Vector Products  in 3-dimensional {E}uclidean Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {381--383},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIX_4.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Yamazaki, Hiroshi},
      TITLE   = {Calculation of Matrices of Field Elements. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {385--391},
      NUMBER  = {{\bf 4}})

@ARTICLE(LFUZZY_0.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Bancerek, Grzegorz},
      TITLE   = {Lattice of Fuzzy Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {393--398},
      NUMBER  = {{\bf 4}})

@ARTICLE(KURATO_2.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {On the {K}uratowski Limit Operators},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {399--409},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN_A.ABS,
      AUTHOR  = {Trybulec, Andrzej},
      TITLE   = {On the Segmentation of a Simple Closed Curve},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {411--416},
      NUMBER  = {{\bf 4}})

@ARTICLE(BINARI_5.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {On the Calculus of Binary Arithmetics},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {417--419},
      NUMBER  = {{\bf 4}})

@ARTICLE(SCMPDS_9.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Shidama, Yasunari},
      TITLE   = {{SCMPDS} Is Not Standard},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {421--424},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN19.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {On the Upper and Lower Approximations of the Curve},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2003},
      VOLUME  = 11,
      PAGES   = {425--430},
      NUMBER  = {{\bf 4}})

@ARTICLE(RFINSEQ2.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Sorting Operators for Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {1--4},
      NUMBER  = {{\bf 1}})

@ARTICLE(RADIX_5.ABS,
      AUTHOR  = {Niimura, Masaaki and Fuwa, Yasushi},
      TITLE   = {Magnitude Relation Properties of Radix-$2^k$ {SD} Number},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {5--8},
      NUMBER  = {{\bf 1}})

@ARTICLE(RADIX_6.ABS,
      AUTHOR  = {Niimura, Masaaki and Fuwa, Yasushi},
      TITLE   = {High Speed Modulo Calculation Algorithm with Radix-$2^k$ {SD} Number},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {9--13},
      NUMBER  = {{\bf 1}})

@ARTICLE(LFUZZY_1.ABS,
      AUTHOR  = {Mitsuishi, Takashi and Bancerek, Grzegorz},
      TITLE   = {Transitive Closure of Fuzzy Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {15--20},
      NUMBER  = {{\bf 1}})

@ARTICLE(ROUGHS_1.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {Basic Properties of Rough Sets and Rough Membership Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {21--28},
      NUMBER  = {{\bf 1}})

@ARTICLE(PRGCOR_1.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Correctness of Non Overwriting Programs. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {29--32},
      NUMBER  = {{\bf 1}})

@ARTICLE(AMISTD_3.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {A Tree of Execution of a Macroinstruction},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {33--37},
      NUMBER  = {{\bf 1}})

@ARTICLE(LOPBAN_1.ABS,
      AUTHOR  = {Shidama, Yasunari},
      TITLE   = {Banach Space of Bounded Linear Operators},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {39--48},
      NUMBER  = {{\bf 1}})

@ARTICLE(UPROOTS.ABS,
      AUTHOR  = {Rudnicki, Piotr},
      TITLE   = {Little {B}ezout Theorem (Factor Theorem)},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {49--58},
      NUMBER  = {{\bf 1}})

@ARTICLE(UNIROOTS.ABS,
      AUTHOR  = {Arneson, Broderick and Rudnicki, Piotr},
      TITLE   = {Primitive Roots of Unity and Cyclotomic Polynomials},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {59--67},
      NUMBER  = {{\bf 1}})

@ARTICLE(WEDDWITT.ABS,
      AUTHOR  = {Arneson, Broderick and Baaz, Matthias and Rudnicki, Piotr},
      TITLE   = {Witt's Proof of the {W}edderburn Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {69--75},
      NUMBER  = {{\bf 1}})

@ARTICLE(RSSPACE4.ABS,
      AUTHOR  = {Suzuki, Yasumasa},
      TITLE   = {Banach Space of Bounded Real Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {77--83},
      NUMBER  = {{\bf 2}})

@ARTICLE(POLYEQ_3.ABS,
      AUTHOR  = {Ding, Yuzhong and Liang, Xiquan},
      TITLE   = {Solving Roots of Polynomial Equation  of Degree 2 and 3 with Complex Coefficients},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {85--92},
      NUMBER  = {{\bf 2}})

@ARTICLE(CLVECT_1.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Complex Linear Space and Complex Normed Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {93--102},
      NUMBER  = {{\bf 2}})

@ARTICLE(LOPBAN_2.ABS,
      AUTHOR  = {Shidama, Yasunari},
      TITLE   = {The {B}anach Algebra of Bounded Linear Operators},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {103--108},
      NUMBER  = {{\bf 2}})

@ARTICLE(CSSPACE.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Complex Linear Space of Complex Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {109--117},
      NUMBER  = {{\bf 2}})

@ARTICLE(JORDAN20.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Behaviour of an Arc Crossing a Line},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {119--124},
      NUMBER  = {{\bf 2}})

@ARTICLE(FINTOPO3.ABS,
      AUTHOR  = {Tanaka, Masami and Nakamura, Yatsuka},
      TITLE   = {Some Set Series  in Finite Topological Spaces.  {F}undamental Concepts for Image Processing},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {125--129},
      NUMBER  = {{\bf 2}})

@ARTICLE(LOPBAN_3.ABS,
      AUTHOR  = {Shidama, Yasunari},
      TITLE   = {The Series on {B}anach Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {131--138},
      NUMBER  = {{\bf 2}})

@ARTICLE(SIN_COS4.ABS,
      AUTHOR  = {Chanapat, Pacharapokin and Kanchun,  and Yamazaki, Hiroshi},
      TITLE   = {Formulas and Identities of Trigonometric Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {139--141},
      NUMBER  = {{\bf 2}})

@ARTICLE(NECKLA_3.ABS,
      AUTHOR  = {Retel, Krzysztof},
      TITLE   = {The Class of Series-Parallel Graphs.  {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {143--149},
      NUMBER  = {{\bf 2}})

@ARTICLE(SCMRING4.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Shidama, Yasunari},
      TITLE   = {Relocability for {SCM} over Ring},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {151--157},
      NUMBER  = {{\bf 2}})

@ARTICLE(CLVECT_2.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Convergent Sequences in Complex Unitary Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {159--165},
      NUMBER  = {{\bf 2}})

@ARTICLE(RECDEF_2.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Recursive Definitions. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {167--172},
      NUMBER  = {{\bf 2}})

@ARTICLE(LOPBAN_4.ABS,
      AUTHOR  = {Shidama, Yasunari},
      TITLE   = {The Exponential Function on {B}anach Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {173--177},
      NUMBER  = {{\bf 2}})

@ARTICLE(NAT_3.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Rudnicki, Piotr},
      TITLE   = {Fundamental {T}heorem of {A}rithmetic},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {179--186},
      NUMBER  = {{\bf 2}})

@ARTICLE(CSSPACE2.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Hilbert Space of Complex Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {187--190},
      NUMBER  = {{\bf 2}})

@ARTICLE(CSSPACE3.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Banach Space of Absolute Summable Complex Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {191--194},
      NUMBER  = {{\bf 2}})

@ARTICLE(TAYLOR_1.ABS,
      AUTHOR  = {Shidama, Yasunari},
      TITLE   = {The {T}aylor Expansions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {195--200},
      NUMBER  = {{\bf 2}})

@ARTICLE(CLOPBAN1.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Complex {B}anach Space of Bounded Linear Operators},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {201--209},
      NUMBER  = {{\bf 2}})

@ARTICLE(CSSPACE4.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Complex {B}anach Space of Bounded Complex Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {211--218},
      NUMBER  = {{\bf 2}})

@ARTICLE(FINSEQ_8.ABS,
      AUTHOR  = {Fukura, Hirofumi and Nakamura, Yatsuka},
      TITLE   = {Concatenation of Finite Sequences Reducing Overlapping Part and an Argument  of Separators of Sequential Files},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {219--224},
      NUMBER  = {{\bf 2}})

@ARTICLE(CLVECT_3.ABS,
      AUTHOR  = {Suzuki, Yasumasa and Endou, Noboru},
      TITLE   = {Cauchy Sequence of Complex Unitary Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {225--229},
      NUMBER  = {{\bf 2}})

@ARTICLE(CFUNCDOM.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Complex Valued Functions Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {231--235},
      NUMBER  = {{\bf 3}})

@ARTICLE(CLOPBAN2.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Banach Algebra of Bounded Complex Linear Operators},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {237--242},
      NUMBER  = {{\bf 3}})

@ARTICLE(SIN_COS5.ABS,
      AUTHOR  = {Ding, Yuzhong and Liang, Xiquan},
      TITLE   = {Formulas and Identities of Trigonometric Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {243--246},
      NUMBER  = {{\bf 3}})

@ARTICLE(POLYEQ_4.ABS,
      AUTHOR  = {Ding, Yuzhong and Liang, Xiquan},
      TITLE   = {Solving Roots of the Special Polynomial Equation with Real Coefficients},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {247--250},
      NUMBER  = {{\bf 3}})

@ARTICLE(BORSUK_6.ABS,
      AUTHOR  = {Grabowski, Adam and Korni{\l}owicz, Artur},
      TITLE   = {Algebraic Properties of Homotopies},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {251--260},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPALG_1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Shidama, Yasunari and Grabowski, Adam},
      TITLE   = {The Fundamental Group},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {261--268},
      NUMBER  = {{\bf 3}})

@ARTICLE(NFCONT_1.ABS,
      AUTHOR  = {Nishiyama, Takaya and Ohkubo, Keiji and Shidama, Yasunari},
      TITLE   = {The Continuous Functions on Normed Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {269--275},
      NUMBER  = {{\bf 3}})

@ARTICLE(NFCONT_2.ABS,
      AUTHOR  = {Nishiyama, Takaya and Korni{\l}owicz, Artur and Shidama, Yasunari},
      TITLE   = {The Uniform Continuity of Functions on Normed Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {277--279},
      NUMBER  = {{\bf 3}})

@ARTICLE(CLOPBAN3.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Series on Complex {B}anach Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {281--288},
      NUMBER  = {{\bf 3}})

@ARTICLE(CLOPBAN4.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Exponential Function on Complex {B}anach Algebra},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {289--293},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPALG_2.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Fundamental Group of Convex Subspaces of ${\calE}^n_{\rmT}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {295--299},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPREAL9.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Shidama, Yasunari},
      TITLE   = {Intersections of Intervals and Balls in ${\calE}^n_{\rmT}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {301--306},
      NUMBER  = {{\bf 3}})

@ARTICLE(FIB_NUM2.ABS,
      AUTHOR  = {Jastrz\c{e}bska, Magdalena and Grabowski, Adam},
      TITLE   = {Some Properties of {F}ibonacci Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {307--313},
      NUMBER  = {{\bf 3}})

@ARTICLE(HALLMAR1.ABS,
      AUTHOR  = {Romanowicz, Ewa and Grabowski, Adam},
      TITLE   = {The {H}all {M}arriage {T}heorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {315--320},
      NUMBER  = {{\bf 3}})

@ARTICLE(NDIFF_1.ABS,
      AUTHOR  = {Imura, Hiroshi and Kimura, Morishige and Shidama, Yasunari},
      TITLE   = {The Differentiable Functions on Normed Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {321--327},
      NUMBER  = {{\bf 3}})

@ARTICLE(FIB_NUM3.ABS,
      AUTHOR  = {Wojtecki, Piotr and Grabowski, Adam},
      TITLE   = {Lucas Numbers and Generalized {F}ibonacci Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {329--333},
      NUMBER  = {{\bf 3}})

@ARTICLE(LATSUM_1.ABS,
      AUTHOR  = {Romanowicz, Katarzyna and Grabowski, Adam},
      TITLE   = {The Operation of Addition of Relational Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {335--339},
      NUMBER  = {{\bf 3}})

@ARTICLE(NAGATA_1.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {The {N}agata-{S}mirnov Theorem. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {341--346},
      NUMBER  = {{\bf 3}})

@ARTICLE(GROUP_8.ABS,
      AUTHOR  = {Geleijnse, Gijs and Bancerek, Grzegorz},
      TITLE   = {Properties of Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {347--350},
      NUMBER  = {{\bf 3}})

@ARTICLE(CATALAN1.ABS,
      AUTHOR  = {Cz\k{e}stochowska, Dorota and Grabowski, Adam},
      TITLE   = {Catalan Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {351--353},
      NUMBER  = {{\bf 3}})

@ARTICLE(SHEFFER1.ABS,
      AUTHOR  = {Kozarkiewicz, Violetta and Grabowski, Adam},
      TITLE   = {Axiomatization of {B}oolean Algebras Based on {S}heffer Stroke},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {355--361},
      NUMBER  = {{\bf 3}})

@ARTICLE(SHEFFER2.ABS,
      AUTHOR  = {{\L}ukaszuk, Aneta and Grabowski, Adam},
      TITLE   = {Short {S}heffer Stroke-Based Single Axiom for {B}oolean Algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {363--370},
      NUMBER  = {{\bf 3}})

@ARTICLE(NDIFF_2.ABS,
      AUTHOR  = {Imura, Hiroshi and Sakai, Yuji and Shidama, Yasunari},
      TITLE   = {Differentiable Functions on Normed Linear Spaces. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {371--374},
      NUMBER  = {{\bf 3}})

@ARTICLE(PRGCOR_2.ABS,
      AUTHOR  = {Nishiyama, Takaya and Fukura, Hirofumi and Nakamura, Yatsuka},
      TITLE   = {Logical Correctness of Vector Calculation Programs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {375--380},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINTOPO4.ABS,
      AUTHOR  = {Imura, Hiroshi and Tanaka, Masami and Nakamura, Yatsuka},
      TITLE   = {Continuous Mappings between Finite and One-Dimensional Finite Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {381--384},
      NUMBER  = {{\bf 3}})

@ARTICLE(NAGATA_2.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {The {N}agata-{S}mirnov Theorem. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {385--389},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPALG_3.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Isomorphism of Fundamental Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {391--396},
      NUMBER  = {{\bf 3}})

@ARTICLE(VFUNCT_2.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Algebra of Complex Vector Valued Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {397--401},
      NUMBER  = {{\bf 3}})

@ARTICLE(NCFCONT1.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Continuous Functions on Real and Complex Normed Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {403--419},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPALG_4.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Fundamental Groups of Products of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2004},
      VOLUME  = 12,
      PAGES   = {421--425},
      NUMBER  = {{\bf 3}})

@ARTICLE(SERIES_2.ABS,
      AUTHOR  = {Liang, Ming and Ding, Yuzhong},
      TITLE   = {Partial Sum of Some Series},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {1--4},
      NUMBER  = {{\bf 1}})

@ARTICLE(SUBSTUT1.ABS,
      AUTHOR  = {Braselmann, Patrick and Koepke, Peter},
      TITLE   = {Substitution in First-Order Formulas: Elementary Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {5--15},
      NUMBER  = {{\bf 1}})

@ARTICLE(SUBLEMMA.ABS,
      AUTHOR  = {Braselmann, Patrick and Koepke, Peter},
      TITLE   = {Coincidence Lemma and Substitution Lemma},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {17--26},
      NUMBER  = {{\bf 1}})

@ARTICLE(SUBSTUT2.ABS,
      AUTHOR  = {Braselmann, Patrick and Koepke, Peter},
      TITLE   = {Substitution in First-Order Formulas.  {P}art {II}.
                 {T}he Construction of First-Order Formulas},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {27--32},
      NUMBER  = {{\bf 1}})

@ARTICLE(CALCUL_1.ABS,
      AUTHOR  = {Braselmann, Patrick and Koepke, Peter},
      TITLE   = {A Sequent Calculus for First-Order Logic},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {33--39},
      NUMBER  = {{\bf 1}})

@ARTICLE(CALCUL_2.ABS,
      AUTHOR  = {Braselmann, Patrick and Koepke, Peter},
      TITLE   = {Consequences of the Sequent Calculus},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {41--44},
      NUMBER  = {{\bf 1}})

@ARTICLE(HENMODEL.ABS,
      AUTHOR  = {Braselmann, Patrick and Koepke, Peter},
      TITLE   = {Equivalences of Inconsistency and {H}enkin Models},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {45--48},
      NUMBER  = {{\bf 1}})

@ARTICLE(GOEDELCP.ABS,
      AUTHOR  = {Braselmann, Patrick and Koepke, Peter},
      TITLE   = {G{\"o}del's Completeness Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {49--53},
      NUMBER  = {{\bf 1}})

@ARTICLE(BVFUNC26.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {Propositional Calculus for Boolean Valued Functions.
                {P}art {VIII}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {55--58},
      NUMBER  = {{\bf 1}})

@ARTICLE(HOLDER_1.ABS,
      AUTHOR  = {Suzuki, Yasumasa},
      TITLE   = {H\"older's Inequality and {M}inkowski's Inequality},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {59--61},
      NUMBER  = {{\bf 1}})

@ARTICLE(LP_SPACE.ABS,
      AUTHOR  = {Suzuki, Yasumasa},
      TITLE   = {The {B}anach Space $l^p$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {63--66},
      NUMBER  = {{\bf 1}})

@ARTICLE(MESFUNC3.ABS,
      AUTHOR  = {Shidama, Yasunari and Endou, Noboru},
      TITLE   = {Lebesgue Integral of Simple Valued Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {67--71},
      NUMBER  = {{\bf 1}})

@ARTICLE(SIN_COS6.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Shidama, Yasunari},
      TITLE   = {Inverse Trigonometric Functions Arcsin and Arccos},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {73--79},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN21.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On Some Points of a Simple Closed Curve},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {81--87},
      NUMBER  = {{\bf 1}})

@ARTICLE(JORDAN22.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Grabowski, Adam},
      TITLE   = {On Some Points of a Simple Closed Curve. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {89--91},
      NUMBER  = {{\bf 1}})

@ARTICLE(NCFCONT2.ABS,
      AUTHOR  = {Endou, Noboru},
      TITLE   = {Uniform Continuity of Functions on Normed Complex Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {93--98},
      NUMBER  = {{\bf 1}})

@ARTICLE(RLTOPSP1.ABS,
      AUTHOR  = {Byli\'nski, Czes{\l}aw},
      TITLE   = {Introduction to Real Linear Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {99--107},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPREALA.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Shidama, Yasunari},
      TITLE   = {Some Properties of Rectangles on the Plane},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {109--115},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPREALB.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Shidama, Yasunari},
      TITLE   = {Some Properties of Circles on the Plane},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {117--124},
      NUMBER  = {{\bf 1}})

@ARTICLE(PENCIL_3.ABS,
      AUTHOR  = {Naumowicz, Adam},
      TITLE   = {On the Characterization of Collineations of the
                {S}egre Product of Strongly Connected Partial Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {125--131},
      NUMBER  = {{\bf 1}})

@ARTICLE(PENCIL_4.ABS,
      AUTHOR  = {Naumowicz, Adam},
      TITLE   = {Spaces of Pencils, {G}rassmann Spaces, and Generalized {V}eronese Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {133--138},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPGEN_1.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {On the Boundary and Derivative of a Set},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {139--146},
      NUMBER  = {{\bf 1}})

@ARTICLE(GROEB_3.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {Construction of {G}r\"obner Bases:
                Avoiding S-Polynomials -- {B}uchberger's First Criterium},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {147--156},
      NUMBER  = {{\bf 1}})

@ARTICLE(MATRIX_5.ABS,
      AUTHOR  = {Chang, Wenpai and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {A Theory of Matrices of Complex Elements},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {157--162},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPGEN_2.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {On the Characteristic and Weight of a Topological Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {163--169},
      NUMBER  = {{\bf 1}})

@ARTICLE(TOPGEN_3.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {On Constructing Topological Spaces and {S}orgenfrey Line},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {171--179},
      NUMBER  = {{\bf 1}})

@ARTICLE(PARTFUN3.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {On the Real Valued Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {181--187},
      NUMBER  = {{\bf 1}})

@ARTICLE(ROBBINS3.ABS,
      AUTHOR  = {Grabowski, Adam and Moschner, Markus},
      TITLE   = {Formalization of Ortholattices via~Orthoposets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {189--197},
      NUMBER  = {{\bf 1}})

@ARTICLE(JGRAPH_7.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej},
      TITLE   = {The {F}ashoda Meet Theorem for Rectangles},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {199--219},
      NUMBER  = {{\bf 2}})

@ARTICLE(MATHMORP.ABS,
      AUTHOR  = {Ding, Yuzhong and Liang, Xiquan},
      TITLE   = {Preliminaries to Mathematical Morphology and Its Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {221--225},
      NUMBER  = {{\bf 2}})

@ARTICLE(JORDAN23.ABS,
      AUTHOR  = {Milewski, Robert},
      TITLE   = {Subsequences of Almost, Weakly and Poorly One-to-one Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {227--233},
      NUMBER  = {{\bf 2}})

@ARTICLE(GLIB_000.ABS,
      AUTHOR  = {Lee, Gilbert and Rudnicki, Piotr},
      TITLE   = {Alternative Graph Structures},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {235--252},
      NUMBER  = {{\bf 2}})

@ARTICLE(GLIB_001.ABS,
      AUTHOR  = {Lee, Gilbert},
      TITLE   = {Walks in Graphs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {253--269},
      NUMBER  = {{\bf 2}})

@ARTICLE(GLIB_002.ABS,
      AUTHOR  = {Lee, Gilbert},
      TITLE   = {Trees and Graph Components},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {271--277},
      NUMBER  = {{\bf 2}})

@ARTICLE(GLIB_003.ABS,
      AUTHOR  = {Lee, Gilbert},
      TITLE   = {Weighted and Labeled Graphs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {279--293},
      NUMBER  = {{\bf 2}})

@ARTICLE(GLIB_004.ABS,
      AUTHOR  = {Lee, Gilbert and Rudnicki, Piotr},
      TITLE   = {Correctness of {D}ijkstra's Shortest Path and {P}rim's Minimum Spanning Tree Algorithms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {295--304},
      NUMBER  = {{\bf 2}})

@ARTICLE(GLIB_005.ABS,
      AUTHOR  = {Lee, Gilbert},
      TITLE   = {Correctnesss of {F}ord-{F}ulkerson's Maximum Flow Algorithm},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {305--314},
      NUMBER  = {{\bf 2}})

@ARTICLE(RCOMP_3.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Properties of Connected Subsets  of the Real Line},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {315--323},
      NUMBER  = {{\bf 2}})

@ARTICLE(TOPALG_5.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {The Fundamental Group of the Circle},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {325--331},
      NUMBER  = {{\bf 2}})

@ARTICLE(BROUWER.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Shidama, Yasunari},
      TITLE   = {Brouwer Fixed Point Theorem for Disks on the Plane},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {333--336},
      NUMBER  = {{\bf 2}})

@ARTICLE(STIRL2_1.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Stirling Numbers of the Second Kind},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {337--345},
      NUMBER  = {{\bf 2}})

@ARTICLE(SETLIM_1.ABS,
      AUTHOR  = {Zhang, Bo and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {Limit of Sequence of Subsets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {347--352},
      NUMBER  = {{\bf 2}})

@ARTICLE(ISOMICHI.ABS,
      AUTHOR  = {Jastrz\c{e}bska, Magdalena and Grabowski, Adam},
      TITLE   = {The Properties of Supercondensed Sets, Subcondensed Sets and Condensed Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {353--359},
      NUMBER  = {{\bf 2}})

@ARTICLE(RELSET_2.ABS,
      AUTHOR  = {Retel, Krzysztof},
      TITLE   = {Properties of First and Second Order Cutting of Binary Relations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {361--365},
      NUMBER  = {{\bf 3}})

@ARTICLE(COMPLSP2.ABS,
      AUTHOR  = {Chang, Wenpai and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {The Inner Product and Conjugate of Finite Sequences of Complex Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {367--373},
      NUMBER  = {{\bf 3}})

@ARTICLE(RINFSUP1.ABS,
      AUTHOR  = {Zhang, Bo and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {Inferior Limit and Superior Limit of Sequences of Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {375--381},
      NUMBER  = {{\bf 3}})

@ARTICLE(SIN_COS7.ABS,
      AUTHOR  = {Ge, Fuguo and Liang, Xiquan and Ding, Yuzhong},
      TITLE   = {Formulas and Identities of Inverse Hyperbolic Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {383--387},
      NUMBER  = {{\bf 3}})

@ARTICLE(EUCLIDLP.ABS,
      AUTHOR  = {Kubo, Akihiro},
      TITLE   = {Lines on Planes in $n$-Dimensional {E}uclidean Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {389--397},
      NUMBER  = {{\bf 3}})

@ARTICLE(CARD_FIN.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Cardinal Numbers and Finite Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {399--406},
      NUMBER  = {{\bf 3}})

@ARTICLE(SETLIM_2.ABS,
      AUTHOR  = {Zhang, Bo and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {Some Equations Related to the Limit  of Sequence of Subsets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {407--412},
      NUMBER  = {{\bf 3}})

@ARTICLE(SERIES_3.ABS,
      AUTHOR  = {Ge, Fuguo and Liang, Xiquan},
      TITLE   = {On the Partial Product of Series and Related Basic Inequalities},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {413--416},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINTOPO5.ABS,
      AUTHOR  = {Tanaka, Masami and Imura, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {Homeomorphism between Finite Topological Spaces, Two-Dimensional Lattice Spaces and a Fixed Point Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {417--419},
      NUMBER  = {{\bf 3}})

@ARTICLE(TAYLOR_2.ABS,
      AUTHOR  = {Nishino, Akira and Shidama, Yasunari},
      TITLE   = {The {M}aclaurin Expansions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {421--425},
      NUMBER  = {{\bf 3}})

@ARTICLE(FDIFF_4.ABS,
      AUTHOR  = {Zhang, Yan and Liang, Xiquan},
      TITLE   = {Several Differentiable Formulas of Special Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {427--434},
      NUMBER  = {{\bf 3}})

@ARTICLE(PROB_3.ABS,
      AUTHOR  = {Zhang, Bo and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {Set Sequences and Monotone Class},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {435--441},
      NUMBER  = {{\bf 4}})

@ARTICLE(FILEREC1.ABS,
      AUTHOR  = {Fukura, Hirofumi and Nakamura, Yatsuka},
      TITLE   = {A Theory of Sequential Files},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {443--446},
      NUMBER  = {{\bf 4}})

@ARTICLE(CIRCLED1.ABS,
      AUTHOR  = {Zhai, Fahui and Cao, Jianbing and Liang, Xiquan},
      TITLE   = {Circled Sets, Circled Hull, and Circled Family},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {447--451},
      NUMBER  = {{\bf 4}})

@ARTICLE(TOPGEN_4.ABS,
      AUTHOR  = {Grabowski, Adam},
      TITLE   = {On the {B}orel Families of Subsets of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {453--461},
      NUMBER  = {{\bf 4}})

@ARTICLE(MESFUNC4.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Linearity of {L}ebesgue Integral of Simple Valued Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {463--465},
      NUMBER  = {{\bf 4}})

@ARTICLE(JGRAPH_8.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Trybulec, Andrzej and Korni{\l}owicz, Artur},
      TITLE   = {The {F}ashoda Meet Theorem for Continuous Mappings},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {467--469},
      NUMBER  = {{\bf 4}})

@ARTICLE(TIETZE.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur and Bancerek, Grzegorz and Naumowicz, Adam},
      TITLE   = {Tietze {E}xtension {T}heorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {471--475},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN24.ABS,
      AUTHOR  = {Naumowicz, Adam and Bancerek, Grzegorz},
      TITLE   = {Homeomorphisms of {J}ordan Curves},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {477--480},
      NUMBER  = {{\bf 4}})

@ARTICLE(JORDAN.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Jordan Curve Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {481--491},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIXC1.ABS,
      AUTHOR  = {Chang, Wenpai and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {The Inner Product and Conjugate of Matrix of Complex Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {493--499},
      NUMBER  = {{\bf 4}})

@ARTICLE(SERIES_4.ABS,
      AUTHOR  = {Cao, Jianbing and Zhai, Fahui and Liang, Xiquan},
      TITLE   = {Partial Sum and Partial Product of Some Series},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {501--503},
      NUMBER  = {{\bf 4}})

@ARTICLE(FDIFF_5.ABS,
      AUTHOR  = {Cao, Jianbing and Zhai, Fahui and Liang, Xiquan},
      TITLE   = {Some Differentiable Formulas of Special Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {505--509},
      NUMBER  = {{\bf 4}})

@ARTICLE(SIN_COS8.ABS,
      AUTHOR  = {Chanapat, Pacharapokin and Yamazaki, Hiroshi},
      TITLE   = {Formulas and Identities of Hyperbolic Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {511--513},
      NUMBER  = {{\bf 4}})

@ARTICLE(TOPGEN_5.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Niemytzki Plane - an Example of {T}ychonoff Space Which Is Not $T_4$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {515--524},
      NUMBER  = {{\bf 4}})

@ARTICLE(SERIES_5.ABS,
      AUTHOR  = {Ge, Fuguo and Liang, Xiquan},
      TITLE   = {On the Partial Product and Partial Sum of Series and Related Basic Inequalities},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {525--528},
      NUMBER  = {{\bf 4}})

@ARTICLE(FDIFF_6.ABS,
      AUTHOR  = {Zhang, Yan and Li, Bo and Liang, Xiquan},
      TITLE   = {Several Differentiable Formulas of Special Functions. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {529--535},
      NUMBER  = {{\bf 4}})

@ARTICLE(BINARI_6.ABS,
      AUTHOR  = {Kobayashi, Shunichi},
      TITLE   = {On the Calculus of Binary Arithmetics. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {537--540},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIX_6.ABS,
      AUTHOR  = {Yue, Xiaopeng and Liang, Xiquan and Sun, Zhongpin},
      TITLE   = {Some Properties of Some Special Matrices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {541--547},
      NUMBER  = {{\bf 4}})

@ARTICLE(GFACIRC1.ABS,
      AUTHOR  = {Yamaguchi, Shin'nosuke and Wasaki, Katsumi and Shimoi, Nobuhiro},
      TITLE   = {Generalized Full Adder Circuits ({GFA}s). {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {549--571},
      NUMBER  = {{\bf 4}})

@ARTICLE(RING_1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Quotient Rings},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {573--576},
      NUMBER  = {{\bf 4}})

@ARTICLE(REAL_NS1.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Completeness of the Real {E}uclidean Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2005},
      VOLUME  = 13,
      PAGES   = {577--580},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIX_7.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Determinant of Some Matrices  of Field Elements},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0001-4},
      VOLUME  = 14,
      PAGES   = {1--5},
      NUMBER  = {{\bf 1}})

@ARTICLE(MATRIX_8.ABS,
      AUTHOR  = {Yue, Xiaopeng and Hu, Dahai and Liang, Xiquan},
      TITLE   = {Some Properties of Some Special Matrices.  {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0002-3},
      VOLUME  = 14,
      PAGES   = {7--12},
      NUMBER  = {{\bf 1}})

@ARTICLE(MATRIX_9.ABS,
      AUTHOR  = {Romanowicz, Ewa and Grabowski, Adam},
      TITLE   = {On the Permanent of a Matrix},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0003-2},
      VOLUME  = 14,
      PAGES   = {13--20},
      NUMBER  = {{\bf 1}})

@ARTICLE(MATRIXR1.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Tamura, Nobuyuki and Chang, Wenpai},
      TITLE   = {A Theory of Matrices of Real Elements},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0004-1},
      VOLUME  = 14,
      PAGES   = {21--28},
      NUMBER  = {{\bf 1}})

@ARTICLE(MOEBIUS1.ABS,
      AUTHOR  = {Jastrz\c{e}bska, Magdalena and Grabowski, Adam},
      TITLE   = {On the Properties of the {M}\"obius Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0005-0},
      VOLUME  = 14,
      PAGES   = {29--36},
      NUMBER  = {{\bf 1}})

@ARTICLE(FDIFF_7.ABS,
      AUTHOR  = {Li, Bo and Zhang, Yan and Liang, Xiquan},
      TITLE   = {Several Differentiation Formulas  of Special Functions. {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0006-z},
      VOLUME  = 14,
      PAGES   = {37--45},
      NUMBER  = {{\bf 1}})

@ARTICLE(NAT_4.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {Pocklington's Theorem and {B}ertrand's Postulate},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0007-y},
      VOLUME  = 14,
      PAGES   = {47--52},
      NUMBER  = {{\bf 2}})

@ARTICLE(MESFUNC5.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Integral of Measurable Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0008-x},
      VOLUME  = 14,
      PAGES   = {53--70},
      NUMBER  = {{\bf 2}})

@ARTICLE(REAL_3.ABS,
      AUTHOR  = {Li, Bo and Zhang, Yan and Korni{\l}owicz, Artur},
      TITLE   = {Simple Continued Fractions  and Their Convergents},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0009-9},
      VOLUME  = 14,
      PAGES   = {71--78},
      NUMBER  = {{\bf 3}})

@ARTICLE(CHORD.ABS,
      AUTHOR  = {Arneson, Broderick and Rudnicki, Piotr},
      TITLE   = {Chordal Graphs},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0010-3},
      VOLUME  = 14,
      PAGES   = {79--92},
      NUMBER  = {{\bf 3}})

@ARTICLE(FINTOPO6.ABS,
      AUTHOR  = {Nakamura, Yatsuka},
      TITLE   = {Connectedness and Continuous Sequences  in Finite Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0011-2},
      VOLUME  = 14,
      PAGES   = {93--100},
      NUMBER  = {{\bf 3}})

@ARTICLE(MATRPROB.ABS,
      AUTHOR  = {Zhang, Bo and Nakamura, Yatsuka},
      TITLE   = {The Definition of Finite Sequences  and Matrices of Probability, and Addition of Matrices of Real Elements},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0012-1},
      VOLUME  = 14,
      PAGES   = {101--108},
      NUMBER  = {{\bf 3}})

@ARTICLE(FDIFF_8.ABS,
      AUTHOR  = {Li, Bo and Wang, Peng},
      TITLE   = {Several Differentiation Formulas  of Special Functions. {P}art {IV}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0013-0},
      VOLUME  = 14,
      PAGES   = {109--114},
      NUMBER  = {{\bf 3}})

@ARTICLE(DIFF_1.ABS,
      AUTHOR  = {Li, Bo and Zhang, Yan and Liang, Xiquan},
      TITLE   = {Difference and Difference Quotient},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0014-z},
      VOLUME  = 14,
      PAGES   = {115--119},
      NUMBER  = {{\bf 3}})

@ARTICLE(POLYNOM8.ABS,
      AUTHOR  = {Treyderowski, Krzysztof and Schwarzweller, Christoph},
      TITLE   = {Multiplication of Polynomials  using {D}iscrete {F}ourier {T}ransformation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0015-y},
      VOLUME  = 14,
      PAGES   = {121--128},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIX10.ABS,
      AUTHOR  = {Liang, Xiquan and Ge, Fuguo and Yue, Xiaopeng},
      TITLE   = {Some Special Matrices of Real Elements  and Their Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0016-x},
      VOLUME  = 14,
      PAGES   = {129--134},
      NUMBER  = {{\bf 4}})

@ARTICLE(HURWITZ.ABS,
      AUTHOR  = {Schwarzweller, Christoph and Rowi\'{n}ska-Schwarzweller, Agnieszka},
      TITLE   = {Schur's Theorem on the Stability of Networks},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0017-9},
      VOLUME  = 14,
      PAGES   = {135--142},
      NUMBER  = {{\bf 4}})

@ARTICLE(MESFUNC6.ABS,
      AUTHOR  = {Shidama, Yasunari and Endou, Noboru},
      TITLE   = {Integral of Real-Valued  Measurable Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0018-8},
      VOLUME  = 14,
      PAGES   = {143--152},
      NUMBER  = {{\bf 4}})

@ARTICLE(CATALAN2.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {The {C}atalan Numbers. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0019-7},
      VOLUME  = 14,
      PAGES   = {153--159},
      NUMBER  = {{\bf 4}})

@ARTICLE(QUATERNI.ABS,
      AUTHOR  = {Liang, Xiquan and Ge, Fuguo},
      TITLE   = {The Quaternion Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0020-1},
      VOLUME  = 14,
      PAGES   = {161--169},
      NUMBER  = {{\bf 4}})

@ARTICLE(MODELC_1.ABS,
      AUTHOR  = {Ishida, Kazuhisa},
      TITLE   = {Model Checking. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0021-0},
      VOLUME  = 14,
      PAGES   = {171--186},
      NUMBER  = {{\bf 4}})

@ARTICLE(LEXBFS.ABS,
      AUTHOR  = {Arneson, Broderick and Rudnicki, Piotr},
      TITLE   = {Recognizing Chordal Graphs: Lex {BFS} and {MCS}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0022-z},
      VOLUME  = 14,
      PAGES   = {187--205},
      NUMBER  = {{\bf 4}})

@ARTICLE(INTEGRA6.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari and Yamazaki, Masahiko},
      TITLE   = {Integrability and the Integral  of Partial Functions from $\BbbR$ into $\BbbR$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0023-y},
      VOLUME  = 14,
      PAGES   = {207--212},
      NUMBER  = {{\bf 4}})

@ARTICLE(NORMSP_2.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari and Okamura, Katsumasa},
      TITLE   = {Baire's Category Theorem and Some Spaces  Generated from Real Normed Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0024-x},
      VOLUME  = 14,
      PAGES   = {213--219},
      NUMBER  = {{\bf 4}})

@ARTICLE(NUMERAL1.ABS,
      AUTHOR  = {Naumowicz, Adam},
      TITLE   = {On the Representation of Natural Numbers  in Positional Numeral Systems},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0025-9},
      VOLUME  = 14,
      PAGES   = {221--223},
      NUMBER  = {{\bf 4}})

@ARTICLE(PROB_4.ABS,
      AUTHOR  = {Zhang, Bo and Yamazaki, Hiroshi and Nakamura, Yatsuka},
      TITLE   = {The Relevance of Measure and Probability, and Definition of Completeness of Probability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2006, doi:10.2478/v10037-006-0026-8},
      VOLUME  = 14,
      PAGES   = {225--229},
      NUMBER  = {{\bf 4}})

@ARTICLE(BCIALG_1.ABS,
      AUTHOR  = {Ding, Yuzhong},
      TITLE   = {Several Classes of {BCI}-algebras  and their Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0001-z},
      VOLUME  = 15,
      PAGES   = {1--9},
      NUMBER  = {{\bf 1}})

@ARTICLE(FLANG_1.ABS,
      AUTHOR  = {Trybulec, Micha{\l}},
      TITLE   = {Formal Languages -- Concatenation and Closure},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0002-y},
      VOLUME  = 15,
      PAGES   = {11--15},
      NUMBER  = {{\bf 1}})

@ARTICLE(MATRIX11.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Basic Properties of Determinants  of Square Matrices over a Field},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0003-x},
      VOLUME  = 15,
      PAGES   = {17--25},
      NUMBER  = {{\bf 1}})

@ARTICLE(COMBGRAS.ABS,
      AUTHOR  = {Owsiejczuk, Andrzej},
      TITLE   = {Combinatorial {G}rassmannians},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0004-9},
      VOLUME  = 15,
      PAGES   = {27--33},
      NUMBER  = {{\bf 2}})

@ARTICLE(GROUP_9.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {The {J}ordan-{H}\"older Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0005-8},
      VOLUME  = 15,
      PAGES   = {35--51},
      NUMBER  = {{\bf 2}})

@ARTICLE(FLANG_2.ABS,
      AUTHOR  = {Trybulec, Micha{\l}},
      TITLE   = {Regular Expression Quantifiers -- $m$ to $n$ Occurrences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0006-7},
      VOLUME  = 15,
      PAGES   = {53--58},
      NUMBER  = {{\bf 2}})

@ARTICLE(INTEGRA7.ABS,
      AUTHOR  = {Shidama, Yasunari and Endou, Noboru and Wasaki, Katsumi},
      TITLE   = {Riemann Indefinite Integral of Functions  of Real Variable},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0007-6},
      VOLUME  = 15,
      PAGES   = {59--63},
      NUMBER  = {{\bf 2}})

@ARTICLE(PDIFF_1.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari and Miyajima, Keiichi},
      TITLE   = {Partial Differentiation on Normed Linear Spaces ${\calR}^n$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0008-5},
      VOLUME  = 15,
      PAGES   = {65--72},
      NUMBER  = {{\bf 2}})

@ARTICLE(FDIFF_9.ABS,
      AUTHOR  = {Wang, Peng and Li, Bo},
      TITLE   = {Several Differentiation Formulas of Special Functions. {P}art {V}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0009-4},
      VOLUME  = 15,
      PAGES   = {73--79},
      NUMBER  = {{\bf 3}})

@ARTICLE(PRVECT_2.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari and Miyajima, Keiichi},
      TITLE   = {The Product Space of Real Normed Spaces and its Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0010-y},
      VOLUME  = 15,
      PAGES   = {81--85},
      NUMBER  = {{\bf 3}})

@ARTICLE(AOFA_000.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Mizar Analysis of Algorithms: {P}reliminaries},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0011-x},
      VOLUME  = 15,
      PAGES   = {87--110},
      NUMBER  = {{\bf 3}})

@ARTICLE(ENTROPY1.ABS,
      AUTHOR  = {Zhang, Bo and Nakamura, Yatsuka},
      TITLE   = {Definition and some Properties of Information Entropy},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0012-9},
      VOLUME  = 15,
      PAGES   = {111--119},
      NUMBER  = {{\bf 3}})

@ARTICLE(REWRITE2.ABS,
      AUTHOR  = {Trybulec, Micha{\l}},
      TITLE   = {String Rewriting Systems},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0013-8},
      VOLUME  = 15,
      PAGES   = {121--126},
      NUMBER  = {{\bf 3}})

@ARTICLE(MATRIXR2.ABS,
      AUTHOR  = {Tamura, Nobuyuki and Nakamura, Yatsuka},
      TITLE   = {Determinant and Inverse of Matrices  of Real Elements},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0014-7},
      VOLUME  = 15,
      PAGES   = {127--136},
      NUMBER  = {{\bf 3}})

@ARTICLE(RANKNULL.ABS,
      AUTHOR  = {Alama, Jesse},
      TITLE   = {The Rank+Nullity Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0015-6},
      VOLUME  = 15,
      PAGES   = {137--142},
      NUMBER  = {{\bf 3}})

@ARTICLE(LAPLACE.ABS,
      AUTHOR  = {P\k{a}k, Karol and Trybulec, Andrzej},
      TITLE   = {Laplace Expansion},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0016-5},
      VOLUME  = 15,
      PAGES   = {143--150},
      NUMBER  = {{\bf 3}})

@ARTICLE(MATRIX12.ABS,
      AUTHOR  = {Liang, Xiquan and Sun, Tao and Hu, Dahai},
      TITLE   = {Some Properties of Line and Column Operations on Matrices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0017-4},
      VOLUME  = 15,
      PAGES   = {151--157},
      NUMBER  = {{\bf 3}})

@ARTICLE(GROUP_10.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {The {S}ylow Theorems},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0018-3},
      VOLUME  = 15,
      PAGES   = {159--165},
      NUMBER  = {{\bf 3}})

@ARTICLE(COMPACT1.ABS,
      AUTHOR  = {Byli{\'n}ski, Czes{\l}aw},
      TITLE   = {Alexandroff One Point Compactification},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0019-2},
      VOLUME  = 15,
      PAGES   = {167--170},
      NUMBER  = {{\bf 4}})

@ARTICLE(ARROW.ABS,
      AUTHOR  = {Wiedijk, Freek},
      TITLE   = {Arrow's Impossibility Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0020-9},
      VOLUME  = 15,
      PAGES   = {171--174},
      NUMBER  = {{\bf 4}})

@ARTICLE(BCIALG_2.ABS,
      AUTHOR  = {Ding, Yuzhong and Pang, Zhiyong},
      TITLE   = {Congruences and Quotient Algebras  of {BCI}-algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0021-8},
      VOLUME  = 15,
      PAGES   = {175--180},
      NUMBER  = {{\bf 4}})

@ARTICLE(INT_4.ABS,
      AUTHOR  = {Liang, Xiquan and Yan, Li and Zhao, Junjie},
      TITLE   = {Linear Congruence Relation  and Complete Residue Systems},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0022-7},
      VOLUME  = 15,
      PAGES   = {181--187},
      NUMBER  = {{\bf 4}})

@ARTICLE(INTEGRA8.ABS,
      AUTHOR  = {Peng, Cuiying and Ge, Fuguo and Liang, Xiquan},
      TITLE   = {Several Integrability Formulas  of Special Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0023-6},
      VOLUME  = 15,
      PAGES   = {189--198},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIX13.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Basic Properties of the Rank  of Matrices over a Field},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0024-5},
      VOLUME  = 15,
      PAGES   = {199--211},
      NUMBER  = {{\bf 4}})

@ARTICLE(PCS_0.ABS,
      AUTHOR  = {Grue, Klaus E. and Korni{\l}owicz, Artur},
      TITLE   = {Basic Operations on Preordered  Coherent Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0025-4},
      VOLUME  = 15,
      PAGES   = {213--230},
      NUMBER  = {{\bf 4}})

@ARTICLE(RINFSUP2.ABS,
      AUTHOR  = {Yamazaki, Hiroshi and Endou, Noboru and Shidama, Yasunari and Okazaki, Hiroyuki},
      TITLE   = {Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0026-3},
      VOLUME  = 15,
      PAGES   = {231--236},
      NUMBER  = {{\bf 4}})

@ARTICLE(BCIALG_3.ABS,
      AUTHOR  = {Sun, Tao and Hu, Dahai and Liang, Xiquan},
      TITLE   = {Several Classes of {BCK}-algebras  and their Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0027-2},
      VOLUME  = 15,
      PAGES   = {237--242},
      NUMBER  = {{\bf 4}})

@ARTICLE(FDIFF_10.ABS,
      AUTHOR  = {Li, Bo and Wang, Pan},
      TITLE   = {Several Differentiation Formulas  of Special Functions. {P}art {VI}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2007, doi:10.2478/v10037-007-0028-1},
      VOLUME  = 15,
      PAGES   = {243--250},
      NUMBER  = {{\bf 4}})

@ARTICLE(BSPACE.ABS,
      AUTHOR  = {Alama, Jesse},
      TITLE   = {The Vector Space of Subsets of a Set Based on Symmetric Difference},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0001-7},
      VOLUME  = 16,
      PAGES   = {1--5},
      NUMBER  = {{\bf 1}})

@ARTICLE(POLYFORM.ABS,
      AUTHOR  = {Alama, Jesse},
      TITLE   = {Euler's Polyhedron Formula},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0002-6},
      VOLUME  = 16,
      PAGES   = {7--17},
      NUMBER  = {{\bf 1}})

@ARTICLE(LOPBAN_5.ABS,
      AUTHOR  = {Sakurai, Hideki and Kunimune, Hisayoshi and Shidama, Yasunari},
      TITLE   = {Uniform Boundedness Principle},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0003-5},
      VOLUME  = 16,
      PAGES   = {19--21},
      NUMBER  = {{\bf 1}})

@ARTICLE(INT_5.ABS,
      AUTHOR  = {Yan, Li and Liang, Xiquan and Zhao, Junjie},
      TITLE   = {Gauss Lemma and Law of Quadratic Reciprocity},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0004-4},
      VOLUME  = 16,
      PAGES   = {23--28},
      NUMBER  = {{\bf 1}})

@ARTICLE(FLANG_3.ABS,
      AUTHOR  = {Trybulec, Micha{\l}},
      TITLE   = {Regular Expression Quantifiers -- at least $m$ Occurrences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0005-3},
      VOLUME  = 16,
      PAGES   = {29--33},
      NUMBER  = {{\bf 1}})

@ARTICLE(COMPL_SP.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Complete Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0006-2},
      VOLUME  = 16,
      PAGES   = {35--43},
      NUMBER  = {{\bf 1}})

@ARTICLE(DIFF_2.ABS,
      AUTHOR  = {Li, Bo and Zhuang, Yanping and Liang, Xiquan},
      TITLE   = {Difference and Difference Quotient. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0007-1},
      VOLUME  = 16,
      PAGES   = {45--49},
      NUMBER  = {{\bf 1}})

@ARTICLE(MESFUNC7.ABS,
      AUTHOR  = {Narita, Keiko and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {The First Mean Value Theorem for Integrals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0008-0},
      VOLUME  = 16,
      PAGES   = {51--55},
      NUMBER  = {{\bf 1}})

@ARTICLE(MESFUNC8.ABS,
      AUTHOR  = {Endou, Noboru and Shidama, Yasunari and Narita, Keiko},
      TITLE   = {Egoroff's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0009-z},
      VOLUME  = 16,
      PAGES   = {57--63},
      NUMBER  = {{\bf 1}})

@ARTICLE(BCIALG_4.ABS,
      AUTHOR  = {Sun, Tao and Zhao, Junjie and Liang, Xiquan},
      TITLE   = {BCI-algebras with Condition ({S})  and their Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0010-6},
      VOLUME  = 16,
      PAGES   = {65--71},
      NUMBER  = {{\bf 1}})

@ARTICLE(GFACIRC2.ABS,
      AUTHOR  = {Wasaki, Katsumi},
      TITLE   = {Stability of $n$-Bit Generalized Full Adder Circuits ({GFA}s). {P}art~{II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0011-5},
      VOLUME  = 16,
      PAGES   = {73--80},
      NUMBER  = {{\bf 1}})

@ARTICLE(MATRIX15.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Solutions of Linear Equations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0012-4},
      VOLUME  = 16,
      PAGES   = {81--90},
      NUMBER  = {{\bf 1}})

@ARTICLE(HELLY.ABS,
      AUTHOR  = {Enright, Jessica and Rudnicki, Piotr},
      TITLE   = {Helly Property for Subtrees},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0013-3},
      VOLUME  = 16,
      PAGES   = {91--96},
      NUMBER  = {{\bf 2}})

@ARTICLE(EUCLID_6.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {Heron's Formula and {P}tolemy's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0014-2},
      VOLUME  = 16,
      PAGES   = {97--101},
      NUMBER  = {{\bf 2}})

@ARTICLE(INT_7.ABS,
      AUTHOR  = {Okazaki, Hiroyuki and Shidama, Yasunari},
      TITLE   = {Uniqueness of Factoring an Integer and Multiplicative Group ${{\mathbb Z}}/p{{\mathbb Z}^\ast}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0015-1},
      VOLUME  = 16,
      PAGES   = {103--107},
      NUMBER  = {{\bf 2}})

@ARTICLE(BCIIDEAL.ABS,
      AUTHOR  = {Wu, Chenglong and Ding, Yuzhong},
      TITLE   = {Ideals of {BCI}-algebras and their Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0016-0},
      VOLUME  = 16,
      PAGES   = {109--114},
      NUMBER  = {{\bf 2}})

@ARTICLE(C0SP1.ABS,
      AUTHOR  = {Shidama, Yasunari and Suzuki, Hikofumi and Endou, Noboru},
      TITLE   = {Banach Algebra of Bounded Functionals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0017-z},
      VOLUME  = 16,
      PAGES   = {115--122},
      NUMBER  = {{\bf 2}})

@ARTICLE(CONVEX4.ABS,
      AUTHOR  = {Matsuzaki, Hidenori and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Convex Sets and Convex Combinations  on Complex Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0018-y},
      VOLUME  = 16,
      PAGES   = {123--133},
      NUMBER  = {{\bf 2}})

@ARTICLE(QUATERN2.ABS,
      AUTHOR  = {Ge, Fuguo},
      TITLE   = {Inner Products, Group, Ring  of Quaternion Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0019-x},
      VOLUME  = 16,
      PAGES   = {135--139},
      NUMBER  = {{\bf 2}})

@ARTICLE(HFDIFF_1.ABS,
      AUTHOR  = {Zhao, Junjie and Liang, Xiquan and Yan, Li},
      TITLE   = {Several Higher Differentiation Formulas  of Special Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0020-4},
      VOLUME  = 16,
      PAGES   = {141--145},
      NUMBER  = {{\bf 2}})

@ARTICLE(SIN_COS9.ABS,
      AUTHOR  = {Liang, Xiquan and Xie, Bing},
      TITLE   = {Inverse Trigonometric Functions  Arctan and Arccot},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0021-3},
      VOLUME  = 16,
      PAGES   = {147--158},
      NUMBER  = {{\bf 2}})

@ARTICLE(SINCOS10.ABS,
      AUTHOR  = {Xie, Bing and Liang, Xiquan and Ge, Fuguo},
      TITLE   = {Inverse Trigonometric Functions  Arcsec and Arccosec},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0022-2},
      VOLUME  = 16,
      PAGES   = {159--165},
      NUMBER  = {{\bf 2}})

@ARTICLE(MESFUNC9.ABS,
      AUTHOR  = {Endou, Noboru and Narita, Keiko and Shidama, Yasunari},
      TITLE   = {The {L}ebesgue Monotone Convergence Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0023-1},
      VOLUME  = 16,
      PAGES   = {167--175},
      NUMBER  = {{\bf 2}})

@ARTICLE(AOFA_I00.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Mizar Analysis of Algorithms: Algorithms over Integers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0024-0},
      VOLUME  = 16,
      PAGES   = {177--194},
      NUMBER  = {{\bf 2}})

@ARTICLE(MATRIX14.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Oniumi, Kunio and Chang, Wenpai},
      TITLE   = {Invertibility of Matrices of Field Elements},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0025-z},
      VOLUME  = 16,
      PAGES   = {195--202},
      NUMBER  = {{\bf 2}})

@ARTICLE(RAMSEY_1.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {Ramsey's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0026-y},
      VOLUME  = 16,
      PAGES   = {203--205},
      NUMBER  = {{\bf 2}})

@ARTICLE(ABCMIZ_1.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Towards the Construction of a Model of {M}izar Concepts},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0027-x},
      VOLUME  = 16,
      PAGES   = {207--230},
      NUMBER  = {{\bf 2}})

@ARTICLE(MODELC_2.ABS,
      AUTHOR  = {Ishida, Kazuhisa},
      TITLE   = {Model Checking. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0028-9},
      VOLUME  = 16,
      PAGES   = {231--245},
      NUMBER  = {{\bf 3}})

@ARTICLE(INT_6.ABS,
      AUTHOR  = {Schwarzweller, Christoph},
      TITLE   = {Modular Integer Arithmetic},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0029-8},
      VOLUME  = 16,
      PAGES   = {247--252},
      NUMBER  = {{\bf 3}})

@ARTICLE(BCIALG_5.ABS,
      AUTHOR  = {Sun, Tao and Pan, Weibo and Wu, Chenglong and Liang, Xiquan},
      TITLE   = {General Theory of Quasi-Commutative {BCI}-algebras},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0030-2},
      VOLUME  = 16,
      PAGES   = {253--258},
      NUMBER  = {{\bf 3}})

@ARTICLE(MATRIXJ1.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Block Diagonal Matrices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0031-1},
      VOLUME  = 16,
      PAGES   = {259--267},
      NUMBER  = {{\bf 3}})

@ARTICLE(MATRLIN2.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Linear Map of Matrices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0032-0},
      VOLUME  = 16,
      PAGES   = {269--275},
      NUMBER  = {{\bf 3}})

@ARTICLE(ROBBINS4.ABS,
      AUTHOR  = {M\k{a}dra, El\.zbieta and Grabowski, Adam},
      TITLE   = {Orthomodular Lattices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0033-z},
      VOLUME  = 16,
      PAGES   = {277--282},
      NUMBER  = {{\bf 3}})

@ARTICLE(AFINSQ_2.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Ito, Hisashi},
      TITLE   = {Basic Properties and Concept  of Selected Subsequence  of Zero Based Finite Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0034-y},
      VOLUME  = 16,
      PAGES   = {283--288},
      NUMBER  = {{\bf 3}})

@ARTICLE(VECTSP11.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Eigenvalues of a Linear Transformation},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0035-x},
      VOLUME  = 16,
      PAGES   = {289--295},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIXJ2.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Jordan Matrix Decomposition},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0036-9},
      VOLUME  = 16,
      PAGES   = {297--303},
      NUMBER  = {{\bf 4}})

@ARTICLE(MESFUN10.ABS,
      AUTHOR  = {Endou, Noboru and Narita, Keiko and Shidama, Yasunari},
      TITLE   = {Fatou's Lemma and the {L}ebesgue's Convergence Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0037-8},
      VOLUME  = 16,
      PAGES   = {305--309},
      NUMBER  = {{\bf 4}})

@ARTICLE(INTEGR10.ABS,
      AUTHOR  = {Yamazaki, Masahiko and Yamazaki, Hiroshi and Shidama, Yasunari},
      TITLE   = {Extended {R}iemann Integral of Functions  of Real Variable  and One-sided {L}aplace Transform},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0038-7},
      VOLUME  = 16,
      PAGES   = {311--317},
      NUMBER  = {{\bf 4}})

@ARTICLE(MESFUN6C.ABS,
      AUTHOR  = {Narita, Keiko and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Integral of Complex-Valued Measurable Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0039-6},
      VOLUME  = 16,
      PAGES   = {319--324},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATROID0.ABS,
      AUTHOR  = {Bancerek, Grzegorz and Shidama, Yasunari},
      TITLE   = {Introduction to Matroids},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0040-0},
      VOLUME  = 16,
      PAGES   = {325--332},
      NUMBER  = {{\bf 4}})

@ARTICLE(PDIFF_2.ABS,
      AUTHOR  = {Xie, Bing and Liang, Xiquan and Li, Hongwei},
      TITLE   = {Partial Differentiation of Real Binary Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0041-z},
      VOLUME  = 16,
      PAGES   = {333--338},
      NUMBER  = {{\bf 4}})

@ARTICLE(MODELC_3.ABS,
      AUTHOR  = {Ishida, Kazuhisa and Shidama, Yasunari},
      TITLE   = {Model Checking. {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0042-y},
      VOLUME  = 16,
      PAGES   = {339--353},
      NUMBER  = {{\bf 4}})

@ARTICLE(MATRIX16.ABS,
      AUTHOR  = {Yue, Xiaopeng and Liang, Xiquan},
      TITLE   = {Basic Properties of Circulant Matrices  and Anti-Circular Matrices},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0043-x},
      VOLUME  = 16,
      PAGES   = {355--360},
      NUMBER  = {{\bf 4}})

@ARTICLE(LPSPACE1.ABS,
      AUTHOR  = {Watase, Yasushige and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {On ${L}^1$ Space Formed by Real-Valued Partial Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0044-9},
      VOLUME  = 16,
      PAGES   = {361--369},
      NUMBER  = {{\bf 4}})

@ARTICLE(BCIALG_6.ABS,
      AUTHOR  = {Ding, Yuzhong and Ge, Fuguo and Wu, Chenglong},
      TITLE   = {{BCI}-homomorphisms},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0045-8},
      VOLUME  = 16,
      PAGES   = {371--376},
      NUMBER  = {{\bf 4}})

@ARTICLE(FTACELL1.ABS,
      AUTHOR  = {Wasaki, Katsumi},
      TITLE   = {Stability of the 4-2 Binary Addition Circuit Cells. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0046-7},
      VOLUME  = 16,
      PAGES   = {377--387},
      NUMBER  = {{\bf 4}})

@ARTICLE(FDIFF_11.ABS,
      AUTHOR  = {Ge, Fuguo and Xie, Bing},
      TITLE   = {Several Differentiation Formulas of Special Functions. {P}art {VII}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0047-6},
      VOLUME  = 16,
      PAGES   = {389--399},
      NUMBER  = {{\bf 4}})

@ARTICLE(LOPBAN_6.ABS,
      AUTHOR  = {Sakurai, Hideki and Kunimune, Hisayoshi and Shidama, Yasunari},
      TITLE   = {Open Mapping Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2008, doi:10.2478/v10037-008-0048-5},
      VOLUME  = 16,
      PAGES   = {401--403},
      NUMBER  = {{\bf 4}})

@ARTICLE(EUCLID_7.ABS,
      AUTHOR  = {Nakamura, Yatsuka and Korni{\l}owicz, Artur and Oya, Nagato and Shidama, Yasunari},
      TITLE   = {The Real Vector Spaces of Finite Sequences are Finite Dimensional},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi:10.2478/v10037-009-0001-2},
      VOLUME  = 17,
      PAGES   = {1--9},
      NUMBER  = {{\bf 1}})

@ARTICLE(INTEGRA9.ABS,
      AUTHOR  = {Li, Bo and Zhuang, Yanping and Xie, Bing and Wang, Pan},
      TITLE   = {Several Integrability Formulas  of Some Functions,  Orthogonal Polynomials  and Norm Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi:10.2478/v10037-009-0002-1},
      VOLUME  = 17,
      PAGES   = {11--21},
      NUMBER  = {{\bf 1}})

@ARTICLE(INTEGR11.ABS,
      AUTHOR  = {Li, Bo and Zhuang, Yanping and Men, Yanhong and Liang, Xiquan},
      TITLE   = {Several Integrability Formulas of Special Functions. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi:10.2478/v10037-009-0003-0},
      VOLUME  = 17,
      PAGES   = {23--35},
      NUMBER  = {{\bf 1}})

@ARTICLE(PETRI_2.ABS,
      AUTHOR  = {Jitsukawa, Mitsuru and Kawamoto, Pauline N. and Shidama, Yasunari and Nakamura, Yatsuka},
      TITLE   = {Cell {P}etri Net Concepts},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi:10.2478/v10037-009-0004-z},
      VOLUME  = 17,
      PAGES   = {37--42},
      NUMBER  = {{\bf 1}})

@ARTICLE(VALUED_2.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Arithmetic Operations on Functions from Sets into Functional Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi:10.2478/v10037-009-0005-y},
      VOLUME  = 17,
      PAGES   = {43--60},
      NUMBER  = {{\bf 1}})

@ARTICLE(QUATERN3.ABS,
      AUTHOR  = {Li, Bo and Wang, Pan and Liang, Xiquan and Zhuang, Yanping},
      TITLE   = {Some Operations on Quaternion Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0006-x},
      VOLUME  = 17,
      PAGES   = {61--65},
      NUMBER  = {{\bf 2}})

@ARTICLE(CFDIFF_1.ABS,
      AUTHOR  = {Pacharapokin, Chanapat and Yamazaki, Hiroshi and Shidama, Yasunari and Nakamura, Yatsuka},
      TITLE   = {Complex Function Differentiability},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0007-9},
      VOLUME  = 17,
      PAGES   = {67--72},
      NUMBER  = {{\bf 2}})

@ARTICLE(KOLMOG01.ABS,
      AUTHOR  = {Doll, Agnes},
      TITLE   = {Kolmogorov's Zero-One Law},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0008-8},
      VOLUME  = 17,
      PAGES   = {73--77},
      NUMBER  = {{\bf 2}})

@ARTICLE(PDIFF_3.ABS,
      AUTHOR  = {Xie, Bing and Liang, Xiquan and Shen, Xiuzhuan},
      TITLE   = {Second-Order Partial Differentiation  of Real Binary Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0009-7},
      VOLUME  = 17,
      PAGES   = {79--87},
      NUMBER  = {{\bf 2}})

@ARTICLE(MESFUN7C.ABS,
      AUTHOR  = {Narita, Keiko and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {The Measurability of Complex-Valued Functional Sequences},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0010-1},
      VOLUME  = 17,
      PAGES   = {89--97},
      NUMBER  = {{\bf 2}})

@ARTICLE(MEMBER_1.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {Collective Operations on Number-Membered Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0011-0},
      VOLUME  = 17,
      PAGES   = {99--115},
      NUMBER  = {{\bf 2}})

@ARTICLE(POLYEQ_5.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {Solution of Cubic and Quartic Equations},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0012-z},
      VOLUME  = 17,
      PAGES   = {117--122},
      NUMBER  = {{\bf 2}})

@ARTICLE(NAT_5.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {The Perfect Number Theorem  and {W}ilson's Theorem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0013-y},
      VOLUME  = 17,
      PAGES   = {123--128},
      NUMBER  = {{\bf 2}})

@ARTICLE(RANDOM_1.ABS,
      AUTHOR  = {Okazaki, Hiroyuki and Shidama, Yasunari},
      TITLE   = {Probability on Finite Set and Real-Valued Random Variables},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0014-x},
      VOLUME  = 17,
      PAGES   = {129--136},
      NUMBER  = {{\bf 2}})

@ARTICLE(MESFUN9C.ABS,
      AUTHOR  = {Narita, Keiko and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Lebesgue's Convergence Theorem  of Complex-Valued Function},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0015-9},
      VOLUME  = 17,
      PAGES   = {137--145},
      NUMBER  = {{\bf 2}})

@ARTICLE(CFDIFF_2.ABS,
      AUTHOR  = {Yamazaki, Hiroshi and Shidama, Yasunari and Pacharapokin, Chanapat and Nakamura, Yatsuka},
      TITLE   = {The {C}auchy-{R}iemann Differential Equations of Complex Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0016-8},
      VOLUME  = 17,
      PAGES   = {147--149},
      NUMBER  = {{\bf 2}})

@ARTICLE(GR_CY_3.ABS,
      AUTHOR  = {Arai, Kenichi and Okazaki, Hiroyuki},
      TITLE   = {Properties of Primes and Multiplicative Group of a Field},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0017-7},
      VOLUME  = 17,
      PAGES   = {151--155},
      NUMBER  = {{\bf 2}})

@ARTICLE(MEASURE8.ABS,
      AUTHOR  = {Endou, Noboru and Okazaki, Hiroyuki and Shidama, Yasunari},
      TITLE   = {{H}opf Extension Theorem of Measure},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0018-6},
      VOLUME  = 17,
      PAGES   = {157--162},
      NUMBER  = {{\bf 2}})

@ARTICLE(REWRITE3.ABS,
      AUTHOR  = {Trybulec, Micha{\l}},
      TITLE   = {Labelled State Transition Systems},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0019-5},
      VOLUME  = 17,
      PAGES   = {163--171},
      NUMBER  = {{\bf 2}})

@ARTICLE(DIST_1.ABS,
      AUTHOR  = {Okazaki, Hiroyuki},
      TITLE   = {Probability on Finite and Discrete Set and Uniform Distribution},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0020-z},
      VOLUME  = 17,
      PAGES   = {173--178},
      NUMBER  = {{\bf 2}})

@ARTICLE(INTEGR15.ABS,
      AUTHOR  = {Miyajima, Keiichi and Shidama, Yasunari},
      TITLE   = {Riemann Integral of Functions  from $\mathbb{R}$ into $\calR^n$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0021-y},
      VOLUME  = 17,
      PAGES   = {179--185},
      NUMBER  = {{\bf 2}})

@ARTICLE(FUNCT_8.ABS,
      AUTHOR  = {Li, Bo and Men, Yanhong},
      TITLE   = {Basic Properties of Even and Odd Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0022-x},
      VOLUME  = 17,
      PAGES   = {187--192},
      NUMBER  = {{\bf 2}})

@ARTICLE(FSM_3.ABS,
      AUTHOR  = {Trybulec, Micha{\l}},
      TITLE   = {Equivalence of Deterministic and Nondeterministic Epsilon Automata},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0023-9},
      VOLUME  = 17,
      PAGES   = {193--199},
      NUMBER  = {{\bf 2}})

@ARTICLE(METRIZTS.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Basic Properties of Metrizable Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0024-8},
      VOLUME  = 17,
      PAGES   = {201--205},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPDIM_1.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Small Inductive Dimension of Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0025-7},
      VOLUME  = 17,
      PAGES   = {207--212},
      NUMBER  = {{\bf 3}})

@ARTICLE(GROUP_11.ABS,
      AUTHOR  = {Liang, Xiquan and Li, Dailu},
      TITLE   = {On Rough Subgroup of a Group},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0026-6},
      VOLUME  = 17,
      PAGES   = {213--217},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPDIM_2.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {Small Inductive Dimension of Topological Spaces. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0027-5},
      VOLUME  = 17,
      PAGES   = {219--222},
      NUMBER  = {{\bf 3}})

@ARTICLE(DILWORTH.ABS,
      AUTHOR  = {Rudnicki, Piotr},
      TITLE   = {Dilworth's Decomposition Theorem for Posets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0028-4},
      VOLUME  = 17,
      PAGES   = {223--232},
      NUMBER  = {{\bf 4}})

@ARTICLE(INTEGR1C.ABS,
      AUTHOR  = {Yamazaki, Masahiko and Yamazaki, Hiroshi and Wasaki, Katsumi and Shidama, Yasunari},
      TITLE   = {Complex Integral},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0029-3},
      VOLUME  = 17,
      PAGES   = {233--236},
      NUMBER  = {{\bf 4}})

@ARTICLE(INTERVA1.ABS,
      AUTHOR  = {Grabowski, Adam and Jastrz\k{e}bska, Magdalena},
      TITLE   = {On the Lattice of Intervals and Rough Sets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0030-x},
      VOLUME  = 17,
      PAGES   = {237--244},
      NUMBER  = {{\bf 4}})

@ARTICLE(FUNCT_9.ABS,
      AUTHOR  = {Li, Bo and Men, Yanhong and Li, Dailu and Liang, Xiquan},
      TITLE   = {Basic Properties of Periodic Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0031-9},
      VOLUME  = 17,
      PAGES   = {245--248},
      NUMBER  = {{\bf 4}})

@ARTICLE(ORDINAL5.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Epsilon Numbers and {C}antor Normal Form},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2009, doi: 10.2478/v10037-009-0032-8},
      VOLUME  = 17,
      PAGES   = {249--256},
      NUMBER  = {{\bf 4}})
      
@ARTICLE(EUCLID_8.ABS,
      AUTHOR  = {Liang, Xiquan and Zhao, Piqing and Bai, Ou},
      TITLE   = {{V}ector Functions and their Differentiation Formulas in 3-dimensional {E}uclidean Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0001-2},
      VOLUME  = 18,
      PAGES   = {1--10},
      NUMBER  = {{\bf 1}})

@ARTICLE(C0SP2.ABS,
      AUTHOR  = {Kanazashi, Katuhiko and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {{B}anach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0002-1},
      VOLUME  = 18,
      PAGES   = {11--16},
      NUMBER  = {{\bf 1}})

@ARTICLE(ALGSTR_4.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {{F}ree Magmas},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0003-0},
      VOLUME  = 18,
      PAGES   = {17--26},
      NUMBER  = {{\bf 1}})

@ARTICLE(INTEGR12.ABS,
      AUTHOR  = {Li, Bo and Ma, Na},
      TITLE   = {{I}ntegrability Formulas. {P}art {I}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0004-z},
      VOLUME  = 18,
      PAGES   = {27--37},
      NUMBER  = {{\bf 1}})

@ARTICLE(PDIFF_4.ABS,
      AUTHOR  = {Inou\'e, Takao and Xie, Bing and Liang, Xiquan},
      TITLE   = {{P}artial Differentiation of Real Ternary Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0005-y},
      VOLUME  = 18,
      PAGES   = {39--46},
      NUMBER  = {{\bf 1}})

@ARTICLE(POSET_1.ABS,
      AUTHOR  = {Ishida, Kazuhisa and Shidama, Yasunari},
      TITLE   = {{F}ixpoint Theorem for Continuous Functions on Chain-Complete Posets},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0006-x},
      VOLUME  = 18,
      PAGES   = {47--51},
      NUMBER  = {{\bf 1}})

@ARTICLE(GRNILP_1.ABS,
      AUTHOR  = {Li, Dailu and Liang, Xiquan and Men, Yanhong},
      TITLE   = {{N}ilpotent Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0007-9},
      VOLUME  = 18,
      PAGES   = {53--56},
      NUMBER  = {{\bf 1}})

@ARTICLE(DIFF_3.ABS,
      AUTHOR  = {Liang, Xiquan and Tang, Ling},
      TITLE   = {{D}ifference and Difference Quotient. {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0008-8},
      VOLUME  = 18,
      PAGES   = {57--64},
      NUMBER  = {{\bf 1}})

@ARTICLE(ABCMIZ_A.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {{A} Model of {M}izar Concepts -- Unification},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0009-7},
      VOLUME  = 18,
      PAGES   = {65--75},
      NUMBER  = {{\bf 1}})

@ARTICLE(FIB_NUM4.ABS,
      AUTHOR  = {Jastrz\k{e}bska, Magdalena},
      TITLE   = {{R}epresentation of the {F}ibonacci and {L}ucas Numbers in Terms of Floor and Ceiling},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0010-1},
      VOLUME  = 18,
      PAGES   = {77--80},
      NUMBER  = {{\bf 1}})

@ARTICLE(EUCLID_9.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {{T}he Correspondence Between $n$-dimensional {E}uclidean Space and the Product of $n$ Real Lines},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0011-0},
      VOLUME  = 18,
      PAGES   = {81--85},
      NUMBER  = {{\bf 1}})

@ARTICLE(RLAFFIN1.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {{A}ffine Independence in Vector Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0012-z},
      VOLUME  = 18,
      PAGES   = {87--93},
      NUMBER  = {{\bf 1}})

@ARTICLE(SIMPLEX0.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {{A}bstract Simplicial Complexes},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0013-y},
      VOLUME  = 18,
      PAGES   = {95--106},
      NUMBER  = {{\bf 1}})

@ARTICLE(RVSUM_2.ABS,
      AUTHOR  = {Miyajima, Keiichi and Kato, Takahiro},
      TITLE   = {{T}he Sum and Product of Finite Sequences of Complex Numbers},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0014-x},
      VOLUME  = 18,
      PAGES   = {107--111},
      NUMBER  = {{\bf 2}})

@ARTICLE(PDIFF_5.ABS,
      AUTHOR  = {Inou\'e, Takao},
      TITLE   = {{S}econd-Order Partial Differentiation of Real Ternary Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0015-9},
      VOLUME  = 18,
      PAGES   = {113--127},
      NUMBER  = {{\bf 2}})

@ARTICLE(INTEGR13.ABS,
      AUTHOR  = {Li, Bo and Ma, Na and Liang, Xiquan},
      TITLE   = {{I}ntegrability Formulas. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0016-8},
      VOLUME  = 18,
      PAGES   = {129--141},
      NUMBER  = {{\bf 2}})

@ARTICLE(INTEGR14.ABS,
      AUTHOR  = {Li, Bo and Ma, Na},
      TITLE   = {{I}ntegrability Formulas. {P}art {III}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0017-7},
      VOLUME  = 18,
      PAGES   = {143--157},
      NUMBER  = {{\bf 2}})

@ARTICLE(LPSPACE2.ABS,
      AUTHOR  = {Watase, Yasushige and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {{O}n ${L}^p$ Space Formed by Real-Valued Partial Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0018-6},
      VOLUME  = 18,
      PAGES   = {159--169},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPS_4.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {{M}iscellaneous Facts about Open Functions and Continuous Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0019-5},
      VOLUME  = 18,
      PAGES   = {171--174},
      NUMBER  = {{\bf 3}})

@ARTICLE(TOPREALC.ABS,
      AUTHOR  = {Korni{\l}owicz, Artur},
      TITLE   = {{O}n the Continuity of Some Functions},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0020-z},
      VOLUME  = 18,
      PAGES   = {175--183},
      NUMBER  = {{\bf 3}})

@ARTICLE(RLAFFIN2.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {{T}he Geometric Interior in Real Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0021-y},
      VOLUME  = 18,
      PAGES   = {185--188},
      NUMBER  = {{\bf 3}})

@ARTICLE(SIMPLEX1.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {{S}perner's Lemma},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0022-x},
      VOLUME  = 18,
      PAGES   = {189--196},
      NUMBER  = {{\bf 4}})

@ARTICLE(CARDFIN2.ABS,
      AUTHOR  = {Kaliszyk, Cezary},
      TITLE   = {{C}ounting Derangements, Non Bijective Functions and the Birthday Problem},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0023-9},
      VOLUME  = 18,
      PAGES   = {197--200},
      NUMBER  = {{\bf 4}})

@ARTICLE(INTEGR16.ABS,
      AUTHOR  = {Miyajima, Keiichi and Kato, Takahiro and Shidama, Yasunari},
      TITLE   = {{R}iemann Integral of Functions $\mathbb{R}$ into $\mathbb{C}$},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0024-8},
      VOLUME  = 18,
      PAGES   = {201--206},
      NUMBER  = {{\bf 4}})

@ARTICLE(PDIFF_6.ABS,
      AUTHOR  = {Inou\'e, Takao and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {{D}ifferentiation of Vector-Valued Functions on $n$-Dimensional Real Normed Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0025-7},
      VOLUME  = 18,
      PAGES   = {207--212},
      NUMBER  = {{\bf 4}})

@ARTICLE(RANDOM_2.ABS,
      AUTHOR  = {Okazaki, Hiroyuki and Shidama, Yasunari},
      TITLE   = {{P}robability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2010, doi: 10.2478/v10037-010-0026-6},
      VOLUME  = 18,
      PAGES   = {213--217},
      NUMBER  = {{\bf 4}})

@ARTICLE(PDIFF_7.ABS,
      AUTHOR  = {Inou\'e, Takao and Naumowicz, Adam and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Partial Differentiation of Vector-Valued Functions on $n$-Dimensional Real Normed Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0001-x},
      VOLUME  = 19,
      PAGES   = {1--9},
      NUMBER  = {{\bf 1}})

@ARTICLE(GROUPP_1.ABS,
      AUTHOR  = {Liang, Xiquan and Li, Dailu},
      TITLE   = {Some Properties of $p$-Groups and Commutative $p$-Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0002-9},
      VOLUME  = 19,
      PAGES   = {11--15},
      NUMBER  = {{\bf 1}})

@ARTICLE(INTEGR18.ABS,
      AUTHOR  = {Miyajima, Keiichi and Kato, Takahiro and Shidama, Yasunari},
      TITLE   = {Riemann Integral of Functions from $\mathbb{R}$ into Real Normed Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0003-8},
      VOLUME  = 19,
      PAGES   = {17--22},
      NUMBER  = {{\bf 1}})

@ARTICLE(GROUP_12.ABS,
      AUTHOR  = {Okazaki, Hiroyuki and Arai, Kenichi and Shidama, Yasunari},
      TITLE   = {Normal Subgroup of Product of Groups},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0004-7},
      VOLUME  = 19,
      PAGES   = {23--26},
      NUMBER  = {{\bf 1}})

@ARTICLE(MYCIELSK.ABS,
      AUTHOR  = {Rudnicki, Piotr and Stewart, Lorna},
      TITLE   = {{T}he {M}ycielskian of a Graph},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0005-6},
      VOLUME  = 19,
      PAGES   = {27--34},
      NUMBER  = {{\bf 1}})

@ARTICLE(DIFF_4.ABS,
      AUTHOR  = {Liang, Xiquan and Tang, Ling and Jiang, Xichun},
      TITLE   = {{D}ifference and Difference Quotient. {P}art {IV}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0006-5},
      VOLUME  = 19,
      PAGES   = {35--39},
      NUMBER  = {{\bf 1}})

@ARTICLE(MFOLD_1.ABS,
      AUTHOR  = {Riccardi, Marco},
      TITLE   = {The Definition of Topological Manifolds},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0007-4},
      VOLUME  = 19,
      PAGES   = {41--44},
      NUMBER  = {{\bf 1}})

@ARTICLE(NFCONT_3.ABS,
      AUTHOR  = {Okazaki, Hiroyuki and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {More on Continuous Functions on Normed Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0008-3},
      VOLUME  = 19,
      PAGES   = {45--49},
      NUMBER  = {{\bf 1}})

@ARTICLE(PRVECT_3.ABS,
      AUTHOR  = {Okazaki, Hiroyuki and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Cartesian Products of Family of Real Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0009-2},
      VOLUME  = 19,
      PAGES   = {51--59},
      NUMBER  = {{\bf 1}})

@ARTICLE(RLVECT_X.ABS,
      AUTHOR  = {Futa, Yuichi and Okazaki, Hiroyuki and Shidama, Yasunari},
      TITLE   = {Formalization of Integral Linear Space},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0010-9},
      VOLUME  = 19,
      PAGES   = {61--64},
      NUMBER  = {{\bf 1}})

@ARTICLE(PDIFF_8.ABS,
      AUTHOR  = {Inou\'e, Takao and Naumowicz, Adam and Endou, Noboru and Shidama, Yasunari},
      TITLE   = {Partial Differentiation, Differentiation and Continuity on $n$-Dimensional Real Normed Linear Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0011-8},
      VOLUME  = 19,
      PAGES   = {65--68},
      NUMBER  = {{\bf 2}})

@ARTICLE(NDIFF_3.ABS,
      AUTHOR  = {Okazaki, Hiroyuki and Endou, Noboru and Narita, Keiko and Shidama, Yasunari},
      TITLE   = {Differentiable Functions into Real Normed Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0012-7},
      VOLUME  = 19,
      PAGES   = {69--72},
      NUMBER  = {{\bf 2}})

@ARTICLE(CGAMES_1.ABS,
      AUTHOR  = {Nittka, Robin},
      TITLE   = {Conway's Games and Some of their Basic Properties},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0013-6},
      VOLUME  = 19,
      PAGES   = {73--81},
      NUMBER  = {{\bf 2}})

@ARTICLE(ORDINAL6.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Veblen Hierarchy},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0014-5},
      VOLUME  = 19,
      PAGES   = {83--92},
      NUMBER  = {{\bf 2}})

@ARTICLE(EXCHSORT.ABS,
      AUTHOR  = {Bancerek, Grzegorz},
      TITLE   = {Sorting by Exchanging},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0015-4},
      VOLUME  = 19,
      PAGES   = {93--102},
      NUMBER  = {{\bf 2}})

@ARTICLE(MATRTOP1.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {{L}inear Transformations of {E}uclidean Topological Spaces},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0016-3},
      VOLUME  = 19,
      PAGES   = {103--108},
      NUMBER  = {{\bf 2}})

@ARTICLE(MATRTOP2.ABS,
      AUTHOR  = {P\k{a}k, Karol},
      TITLE   = {{L}inear Transformations of {E}uclidean Topological Spaces. {P}art {II}},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0017-2},
      VOLUME  = 19,
      PAGES   = {109--112},
      NUMBER  = {{\bf 2}})

@ARTICLE(LTLAXIO1.ABS,
      AUTHOR  = {Giero, Mariusz},
      TITLE   = {The Axiomatization of Propositional Linear Time Temporal Logic},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0018-1},
      VOLUME  = 19,
      PAGES   = {113--119},
      NUMBER  = {{\bf 2}})

@ARTICLE(CC0SP1.ABS,
      AUTHOR  = {Kanazashi, Katuhiko and Okazaki, Hiroyuki and Shidama, Yasunari},
      TITLE   = {Banach Algebra of Bounded Complex-Valued Functionals},
      JOURNAL = {Formalized Mathematics},
      YEAR    = {2011, doi: 10.2478/v10037-011-0019-0},
      VOLUME  = 19,
      PAGES   = {121--126},
      NUMBER  = {{\bf 2}})