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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 4758-4760
(domain RemainderFn 1 Integer) Merge.kif 4754-4754 domain RemainderFn, 1 and Integer
(domain RemainderFn 2 Integer) Merge.kif 4755-4755 domain RemainderFn, 2 and Integer
(instance RemainderFn BinaryFunction) Merge.kif 4751-4751 instance RemainderFn and BinaryFunction
(instance RemainderFn PartialValuedRelation) Merge.kif 4753-4753 instance RemainderFn and PartialValuedRelation
(range RemainderFn Integer) Merge.kif 4756-4756 range RemainderFn and 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 and "余函数"
(termFormat ChineseLanguage RemainderFn "剩余") domainEnglishFormat.kif 49381-49381 termFormat ChineseLanguage, RemainderFn and "剩余"
(termFormat ChineseTraditionalLanguage RemainderFn "剩餘") domainEnglishFormat.kif 49380-49380 termFormat ChineseTraditionalLanguage, RemainderFn and "剩餘"
(termFormat EnglishLanguage RemainderFn "remainder") domainEnglishFormat.kif 49379-49379 termFormat EnglishLanguage, RemainderFn and "remainder"

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


(<=>
    (equal
        (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
    (equal
        (AdditionFn
            (MultiplicationFn
                (FloorFn
                    (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))
Merge.kif 4762-4764 equal RemainderFn Integer and Integer and Integer equal AdditionFn MultiplicationFn FloorFn DivisionFn Integer and Integer and Integer and Integer and Integer
(=>
    (equal
        (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER)
    (equal
        (SignumFn ?NUMBER2)
        (SignumFn ?NUMBER)))
Merge.kif 4766-4768

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 8321-8329
(=>
    (equal
        (GreatestCommonDivisorFn @ROW) ?NUMBER)
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?ELEMENT ?NUMBER) 0))))
Merge.kif 4542-4547
(=>
    (equal
        (GreatestCommonDivisorFn @ROW) ?NUMBER)
    (not
        (exists (?GREATER)
            (and
                (greaterThan ?GREATER ?NUMBER)
                (forall (?ELEMENT)
                    (=>
                        (inList ?ELEMENT
                            (ListFn @ROW))
                        (equal
                            (RemainderFn ?ELEMENT ?GREATER) 0)))))))
Merge.kif 4549-4557
(=>
    (equal
        (LeastCommonMultipleFn @ROW) ?NUMBER)
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?NUMBER ?ELEMENT) 0))))
Merge.kif 4615-4620
(=>
    (equal
        (LeastCommonMultipleFn @ROW) ?NUMBER)
    (not
        (exists (?LESS)
            (and
                (lessThan ?LESS ?NUMBER)
                (forall (?ELEMENT)
                    (=>
                        (inList ?ELEMENT
                            (ListFn @ROW))
                        (equal
                            (RemainderFn ?LESS ?ELEMENT) 0)))))))
Merge.kif 4622-4630
(=>
    (instance ?NUMBER EvenInteger)
    (equal
        (RemainderFn ?NUMBER 2) 0))
Merge.kif 4770-4772
(=>
    (instance ?NUMBER OddInteger)
    (equal
        (RemainderFn ?NUMBER 2) 1))
Merge.kif 4774-4776
(=>
    (instance ?PRIME PrimeNumber)
    (forall (?NUMBER)
        (=>
            (equal
                (RemainderFn ?PRIME ?NUMBER) 0)
            (or
                (equal ?NUMBER 1)
                (equal ?NUMBER ?PRIME)))))
Merge.kif 4778-4785


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