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KB Term:  Term intersection
English Word: 

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 4887-4889
(domain RemainderFn 1 Integer) Merge.kif 4883-4883 The number 1 argument of remainder is an instance of integer
(domain RemainderFn 2 Integer) Merge.kif 4884-4884 The number 2 argument of remainder is an instance of integer
(instance RemainderFn BinaryFunction) Merge.kif 4880-4880 Remainder is an instance of binary function
(instance RemainderFn PartialValuedRelation) Merge.kif 4882-4882 Remainder is an instance of partial valued relation
(range RemainderFn Integer) Merge.kif 4885-4885 The range of remainder is an instance of integer

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 727-727
(termFormat ChineseLanguage RemainderFn "余函数") chinese_format.kif 723-723
(termFormat ChineseLanguage RemainderFn "剩余") domainEnglishFormat.kif 49361-49361
(termFormat ChineseTraditionalLanguage RemainderFn "剩餘") domainEnglishFormat.kif 49360-49360
(termFormat EnglishLanguage RemainderFn "remainder") domainEnglishFormat.kif 49359-49359

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


(<=>
    (equal
        (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
    (equal
        (AdditionFn
            (MultiplicationFn
                (FloorFn
                    (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))
Merge.kif 4891-4893 An integer mod another integer is equal to a third integer if and only if (the largest integer less than or equal to the integer and the other integer and the other integer and the third integer) is equal to the integer
(=>
    (equal
        (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
    (equal
        (SignumFn ?NUMBER2)
        (SignumFn ?NUMBER)))
Merge.kif 4895-4897

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


(=>
    (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 8445-8453
(=>
    (equal
        (GreatestCommonDivisorFn @ROW) ?NUMBER)
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?ELEMENT ?NUMBER) 0))))
Merge.kif 4671-4676
(=>
    (equal
        (GreatestCommonDivisorFn @ROW) ?NUMBER)
    (not
        (exists (?GREATER)
            (and
                (greaterThan ?GREATER ?NUMBER)
                (forall (?ELEMENT)
                    (=>
                        (inList ?ELEMENT
                            (ListFn @ROW))
                        (equal
                            (RemainderFn ?ELEMENT ?GREATER) 0)))))))
Merge.kif 4678-4686
(=>
    (equal
        (LeastCommonMultipleFn @ROW) ?NUMBER)
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?NUMBER ?ELEMENT) 0))))
Merge.kif 4744-4749
(=>
    (equal
        (LeastCommonMultipleFn @ROW) ?NUMBER)
    (not
        (exists (?LESS)
            (and
                (lessThan ?LESS ?NUMBER)
                (forall (?ELEMENT)
                    (=>
                        (inList ?ELEMENT
                            (ListFn @ROW))
                        (equal
                            (RemainderFn ?LESS ?ELEMENT) 0)))))))
Merge.kif 4751-4759
(=>
    (instance ?NUMBER EvenInteger)
    (equal
        (RemainderFn ?NUMBER 2) 0))
Merge.kif 4899-4901
(=>
    (instance ?NUMBER OddInteger)
    (equal
        (RemainderFn ?NUMBER 2) 1))
Merge.kif 4903-4905
(=>
    (instance ?PRIME PrimeNumber)
    (forall (?NUMBER)
        (=>
            (equal
                (RemainderFn ?PRIME ?NUMBER) 0)
            (or
                (equal ?NUMBER 1)
                (equal ?NUMBER ?PRIME)))))
Merge.kif 4907-4914


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