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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。") Merge.kif 5258-5259
(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 5255-5257
(domain RemainderFn 1 Integer) Merge.kif 5252-5252 The number 1 argument of remainder is an instance of integer
(domain RemainderFn 2 Integer) Merge.kif 5253-5253 The number 2 argument of remainder is an instance of integer
(instance RemainderFn BinaryFunction) Merge.kif 5249-5249 Remainder is an instance of binary function
(instance RemainderFn PartialValuedRelation) Merge.kif 5251-5251 Remainder is an instance of partial valued relation
(range RemainderFn Integer) Merge.kif 5254-5254 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 445-445
(termFormat ChineseLanguage RemainderFn "余函数") chinese_format.kif 723-723 "余函数" is the printable form of remainder in ChineseLanguage
(termFormat EnglishLanguage RemainderFn "remainder") domainEnglishFormat.kif 8664-8664 "remainder" is the printable form of remainder in english language

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


(<=>
    (equal
        (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
    (equal
        (AdditionFn
            (MultiplicationFn
                (FloorFn
                    (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))
Merge.kif 5261-5263 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 5265-5267

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 9028-9036
(=>
    (equal
        (GreatestCommonDivisorFn @ROW) ?NUMBER)
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?ELEMENT ?NUMBER) 0))))
Merge.kif 5023-5028
(=>
    (equal
        (GreatestCommonDivisorFn @ROW) ?NUMBER)
    (not
        (exists (?GREATER)
            (and
                (greaterThan ?GREATER ?NUMBER)
                (forall (?ELEMENT)
                    (=>
                        (inList ?ELEMENT
                            (ListFn @ROW))
                        (equal
                            (RemainderFn ?ELEMENT ?GREATER) 0)))))))
Merge.kif 5030-5038
(=>
    (equal
        (LeastCommonMultipleFn @ROW) ?NUMBER)
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?NUMBER ?ELEMENT) 0))))
Merge.kif 5102-5107
(=>
    (equal
        (LeastCommonMultipleFn @ROW) ?NUMBER)
    (not
        (exists (?LESS)
            (and
                (lessThan ?LESS ?NUMBER)
                (forall (?ELEMENT)
                    (=>
                        (inList ?ELEMENT
                            (ListFn @ROW))
                        (equal
                            (RemainderFn ?LESS ?ELEMENT) 0)))))))
Merge.kif 5109-5117
(=>
    (instance ?NUMBER EvenInteger)
    (equal
        (RemainderFn ?NUMBER 2) 0))
Merge.kif 5269-5271
(=>
    (instance ?NUMBER OddInteger)
    (equal
        (RemainderFn ?NUMBER 2) 1))
Merge.kif 5273-5275
(=>
    (instance ?PRIME PrimeNumber)
    (forall (?NUMBER)
        (=>
            (equal
                (RemainderFn ?PRIME ?NUMBER) 0)
            (or
                (equal ?NUMBER 1)
                (equal ?NUMBER ?PRIME)))))
Merge.kif 5277-5284


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