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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	If an integer mod another integer is equal to a third integer, then the sign of the other integer is equal to the sign of the third integer

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	If an entity is an instance of leap year and the entity is an instance of the year an integer, then the integer mod 4 is equal to 0 and the integer mod 100 is not equal to 0 or the integer mod 400 is equal to 0
(=> (equal (GreatestCommonDivisorFn @ROW) ?NUMBER) (forall (?ELEMENT) (=> (inList ?ELEMENT (ListFn @ROW)) (equal (RemainderFn ?ELEMENT ?NUMBER) 0))))	Merge.kif 4671-4676	If the greatest common divisor of @ROW is equal to an integer, then for all another integer if the other integer is a member of (@ROW), then the other integer mod the integer is equal to 0
(=> (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	If the greatest common divisor of @ROW is equal to an integer, then there doesn't exist another integer such that the other integer is greater than the integer and for all a third integer if the third integer is a member of (@ROW), then the third integer mod the other integer is equal to 0
(=> (equal (LeastCommonMultipleFn @ROW) ?NUMBER) (forall (?ELEMENT) (=> (inList ?ELEMENT (ListFn @ROW)) (equal (RemainderFn ?NUMBER ?ELEMENT) 0))))	Merge.kif 4744-4749	If the least common multiple of @ROW is equal to an integer, then for all another integer if the other integer is a member of (@ROW), then the integer mod the other integer is equal to 0
(=> (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	If the least common multiple of @ROW is equal to an integer, then there doesn't exist another integer such that the other integer is less than the integer and for all a third integer if the third integer is a member of (@ROW), then the other integer mod the third integer is equal to 0
(=> (instance ?NUMBER EvenInteger) (equal (RemainderFn ?NUMBER 2) 0))	Merge.kif 4899-4901	If an integer is an instance of even integer, then the integer mod 2 is equal to 0
(=> (instance ?NUMBER OddInteger) (equal (RemainderFn ?NUMBER 2) 1))	Merge.kif 4903-4905	If an integer is an instance of odd integer, then the integer mod 2 is equal to 1
(=> (instance ?PRIME PrimeNumber) (forall (?NUMBER) (=> (equal (RemainderFn ?PRIME ?NUMBER) 0) (or (equal ?NUMBER 1) (equal ?NUMBER ?PRIME)))))	Merge.kif 4907-4914	If an integer is an instance of prime number, then for all another integer if the integer mod the other integer is equal to 0, then the other integer is equal to 1 or the other integer is equal to the integer

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