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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 5004-5006
(domain RemainderFn 1 Integer) Merge.kif 5000-5000
(domain RemainderFn 2 Integer) Merge.kif 5001-5001
(instance RemainderFn BinaryFunction) Merge.kif 4997-4997
(instance RemainderFn PartialValuedRelation) Merge.kif 4999-4999
(range RemainderFn Integer) Merge.kif 5002-5002

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
(termFormat ChineseLanguage RemainderFn "余函数") chinese_format.kif 723-723
(termFormat ChineseLanguage RemainderFn "剩余") domainEnglishFormat.kif 49425-49425
(termFormat ChineseTraditionalLanguage RemainderFn "剩餘") domainEnglishFormat.kif 49424-49424
(termFormat EnglishLanguage RemainderFn "remainder") domainEnglishFormat.kif 49423-49423

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


(=>
    (and
        (equal
            (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
        (not
            (equal ?NUMBER2 0)))
    (equal
        (AdditionFn
            (MultiplicationFn
                (FloorFn
                    (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))		 Merge.kif 5008-5019
(=>
    (and
        (equal
            (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
        (not
            (equal ?NUMBER2 0)))
    (equal
        (SignumFn ?NUMBER2)
        (SignumFn ?NUMBER)))		 Merge.kif 5034-5042

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


(=>
    (and
        (equal
            (GreatestCommonDivisorFn @ROW) ?NUMBER)
        (not
            (equal ?NUMBER 0)))
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?ELEMENT ?NUMBER) 0))))		 Merge.kif 4765-4776
(=>
    (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 4778-4792
(=>
    (and
        (equal
            (LeastCommonMultipleFn @ROW) ?NUMBER)
        (not
            (equal ?NUMBER 0)))
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?NUMBER ?ELEMENT) 0))))		 Merge.kif 4850-4860
(=>
    (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 4862-4876
(=>
    (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 8900-8908
(=>
    (and
        (not
            (equal ?NUMBER2 0))
        (equal
            (AdditionFn
                (MultiplicationFn
                    (FloorFn
                        (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))
    (equal
        (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER))		 Merge.kif 5021-5032
(=>
    (instance ?NUMBER EvenInteger)
    (equal
        (RemainderFn ?NUMBER 2) 0))		 Merge.kif 5044-5047
(=>
    (instance ?NUMBER OddInteger)
    (equal
        (RemainderFn ?NUMBER 2) 1))		 Merge.kif 5049-5052
(=>
    (instance ?PRIME PrimeNumber)
    (forall (?NUMBER)
        (=>
            (and
                (equal
                    (RemainderFn ?PRIME ?NUMBER) 0)
                (not
                    (equal ?NUMBER 0)))
            (or
                (equal ?NUMBER 1)
                (equal ?NUMBER ?PRIME)))))		 Merge.kif 5054-5065


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