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KB Term:  Term intersection
English Word: 

  RemainderFn

 Sigma KEE - RemainderFn
RemainderFn

appearance as argument number 1
-------------------------


(documentation RemainderFn ChineseLanguage "(RemainderFn ?NUMBER ?DIVISOR)是数字 ?NUMBER 除以数字 ?DIVISOR 的余数，商数的正负值与 ?DIVISOR 相同。") chinese_format.kif 2267-2268
(documentation RemainderFn EnglishLanguage "(RemainderFn ?NUMBER ?DIVISOR) is the remainder of the number ?NUMBER divided by the number ?DIVISOR. The result has the same sign as ?DIVISOR.") Merge.kif 5101-5103
(documentation RemainderFn JapaneseLanguage "(RemainderFn ?NUMBER ?DIVISOR) は、数値?NUMBER の残りを数値?DIVISORで割った値である。結果の符号は?DIVISOR と同じである。") japanese_format.kif 932-933
(domain RemainderFn 1 Integer) Merge.kif 5097-5097
(domain RemainderFn 2 Integer) Merge.kif 5098-5098
(instance RemainderFn BinaryFunction) Merge.kif 5094-5094
(instance RemainderFn PartialValuedRelation) Merge.kif 5096-5096
(range RemainderFn Integer) Merge.kif 5099-5099

appearance as argument number 2
-------------------------


(format ChineseLanguage RemainderFn "%1 模除 %2") chinese_format.kif 722-722
(format EnglishLanguage RemainderFn "%1 mod %2") english_format.kif 724-724
(format FrenchLanguage RemainderFn "%1 reste %2") french_format.kif 434-434
(format ItalianLanguage RemainderFn "%1 mod %2") relations-it.txt 252-252
(format JapaneseLanguage RemainderFn "%1 を %2 で割った剰余数") japanese_format.kif 2151-2151
(format PortugueseLanguage RemainderFn "%1 mod %2") portuguese_format.kif 386-386
(format cz RemainderFn "%1 mod %2") relations-cz.txt 446-446
(format de RemainderFn "%1 betrag %2") relations-de.txt 935-935
(format hi RemainderFn "%1 aura %2 kaa sheshhaphala") relations-hindi.txt 289-289
(format ro RemainderFn "%1 mod%t{modulo} %2") relations-ro.kif 456-456
(format sv RemainderFn "%1 modulo %2") relations-sv.txt 496-496
(termFormat ChineseLanguage RemainderFn "余函数") chinese_format.kif 723-723
(termFormat ChineseLanguage RemainderFn "剩余") domainEnglishFormat.kif 49444-49444
(termFormat ChineseTraditionalLanguage RemainderFn "剩餘") domainEnglishFormat.kif 49443-49443
(termFormat EnglishLanguage RemainderFn "remainder") domainEnglishFormat.kif 49442-49442

antecedent
-------------------------


(=>
    (and
        (equal
            (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
        (not
            (equal ?NUMBER 0))
        (not
            (equal ?NUMBER1 0))
        (not
            (equal ?NUMBER2 0)))
    (equal
        (SignumFn ?NUMBER2)
        (SignumFn ?NUMBER)))		 Merge.kif 5131-5143
(=>
    (and
        (equal
            (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
        (not
            (equal ?NUMBER2 0)))
    (equal
        (AdditionFn
            (MultiplicationFn
                (FloorFn
                    (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))		 Merge.kif 5105-5116

consequent
-------------------------


(=>
    (and
        (equal
            (GreatestCommonDivisorFn @ROW) ?NUMBER)
        (not
            (equal ?NUMBER 0)))
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?ELEMENT ?NUMBER) 0))))		 Merge.kif 4862-4873
(=>
    (and
        (equal
            (GreatestCommonDivisorFn @ROW) ?NUMBER)
        (not
            (equal ?NUMBER 0)))
    (not
        (exists (?GREATER)
            (and
                (greaterThan ?GREATER ?NUMBER)
                (forall (?ELEMENT)
                    (=>
                        (inList ?ELEMENT
                            (ListFn @ROW))
                        (equal
                            (RemainderFn ?ELEMENT ?GREATER) 0)))))))		 Merge.kif 4875-4889
(=>
    (and
        (equal
            (LeastCommonMultipleFn @ROW) ?NUMBER)
        (not
            (equal ?NUMBER 0)))
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?NUMBER ?ELEMENT) 0))))		 Merge.kif 4947-4957
(=>
    (and
        (equal
            (LeastCommonMultipleFn @ROW) ?NUMBER)
        (not
            (equal ?NUMBER 0)))
    (not
        (exists (?LESS)
            (and
                (lessThan ?LESS ?NUMBER)
                (forall (?ELEMENT)
                    (=>
                        (inList ?ELEMENT
                            (ListFn @ROW))
                        (equal
                            (RemainderFn ?LESS ?ELEMENT) 0)))))))		 Merge.kif 4959-4973
(=>
    (and
        (instance ?LEAP LeapYear)
        (instance ?LEAP
            (YearFn ?NUMBER)))
    (or
        (and
            (equal
                (RemainderFn ?NUMBER 4) 0)
            (not
                (equal
                    (RemainderFn ?NUMBER 100) 0)))
        (equal
            (RemainderFn ?NUMBER 400) 0)))		 Merge.kif 9037-9045
(=>
    (and
        (not
            (equal ?NUMBER2 0))
        (equal
            (AdditionFn
                (MultiplicationFn
                    (FloorFn
                        (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))
    (equal
        (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER))		 Merge.kif 5118-5129
(=>
    (instance ?NUMBER EvenInteger)
    (equal
        (RemainderFn ?NUMBER 2) 0))		 Merge.kif 5145-5148
(=>
    (instance ?NUMBER OddInteger)
    (equal
        (RemainderFn ?NUMBER 2) 1))		 Merge.kif 5150-5153
(=>
    (instance ?PRIME PrimeNumber)
    (forall (?NUMBER)
        (=>
            (and
                (equal
                    (RemainderFn ?PRIME ?NUMBER) 0)
                (not
                    (equal ?NUMBER 0)))
            (or
                (equal ?NUMBER 1)
                (equal ?NUMBER ?PRIME)))))		 Merge.kif 5155-5166


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