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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 5128-5130
(documentation RemainderFn JapaneseLanguage "(RemainderFn ?NUMBER ?DIVISOR) は、数値?NUMBER の残りを数値?DIVISORで割った値である。結果の符号は?DIVISOR と同じである。")	japanese_format.kif 932-933
(domain RemainderFn 1 Integer)	Merge.kif 5124-5124	The number 1 argument of remainder is an instance of integer
(domain RemainderFn 2 Integer)	Merge.kif 5125-5125	The number 2 argument of remainder is an instance of integer
(instance RemainderFn BinaryFunction)	Merge.kif 5121-5121	Remainder is an instance of binary function
(instance RemainderFn PartialValuedRelation)	Merge.kif 5123-5123	Remainder is an instance of partial valued relation
(range RemainderFn Integer)	Merge.kif 5126-5126	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 724-724
(format FrenchLanguage RemainderFn "%1 reste %2")	french_format.kif 434-434
(format ItalianLanguage RemainderFn "%1 mod %2")	relations-it.txt 252-252
(format JapaneseLanguage RemainderFn "%1 を %2 で割った剰余数")	japanese_format.kif 2151-2151
(format PortugueseLanguage RemainderFn "%1 mod %2")	portuguese_format.kif 386-386
(format cz RemainderFn "%1 mod %2")	relations-cz.txt 446-446
(format de RemainderFn "%1 betrag %2")	relations-de.txt 935-935
(format hi RemainderFn "%1 aura %2 kaa sheshhaphala")	relations-hindi.txt 289-289
(format ro RemainderFn "%1 mod%t{modulo} %2")	relations-ro.kif 456-456
(format sv RemainderFn "%1 modulo %2")	relations-sv.txt 496-496
(termFormat ChineseLanguage RemainderFn "余函数")	chinese_format.kif 723-723
(termFormat ChineseLanguage RemainderFn "剩余")	domainEnglishFormat.kif 49446-49446
(termFormat ChineseTraditionalLanguage RemainderFn "剩餘")	domainEnglishFormat.kif 49445-49445
(termFormat EnglishLanguage RemainderFn "remainder")	domainEnglishFormat.kif 49444-49444
(termFormat de RemainderFn "RestFn")	terms-de.txt 286-286

antecedent

(=> (and (equal (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER) (not (equal ?NUMBER 0)) (not (equal ?NUMBER1 0)) (not (equal ?NUMBER2 0))) (equal (SignumFn ?NUMBER2) (SignumFn ?NUMBER)))	Merge.kif 5158-5170	If equal an integer mod another integer and a third integer and equal the third integer and 0 and equal the integer and 0 and equal the other integer and 0, then equal the sign of the other integer and the sign of the third integer
(=> (and (equal (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER) (not (equal ?NUMBER2 0))) (equal (AdditionFn (MultiplicationFn (FloorFn (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1))	Merge.kif 5132-5143	If equal an integer mod another integer and a third integer and equal the other integer and 0, then equal (the largest integer less than or equal to the integer and the other integer and the other integer and the third integer) and the integer

consequent

(=> (and (equal (GreatestCommonDivisorFn @ROW) ?NUMBER) (not (equal ?NUMBER 0))) (forall (?ELEMENT) (=> (inList ?ELEMENT (ListFn @ROW)) (equal (RemainderFn ?ELEMENT ?NUMBER) 0))))	Merge.kif 4889-4900	If equal the greatest common divisor of @ROW and an integer and equal the integer and 0, then for all another integer if the other integer is a member of (@ROW), then equal the other integer mod the integer and 0
(=> (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 4902-4916	If equal the greatest common divisor of @ROW and an integer and equal the integer and 0, 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 equal the third integer mod the other integer and 0
(=> (and (equal (LeastCommonMultipleFn @ROW) ?NUMBER) (not (equal ?NUMBER 0))) (forall (?ELEMENT) (=> (inList ?ELEMENT (ListFn @ROW)) (equal (RemainderFn ?NUMBER ?ELEMENT) 0))))	Merge.kif 4974-4984	If equal the least common multiple of @ROW and an integer and equal the integer and 0, then for all another integer if the other integer is a member of (@ROW), then equal the integer mod the other integer and 0
(=> (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 4986-5000	If equal the least common multiple of @ROW and an integer and equal the integer and 0, 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 equal the other integer mod the third integer and 0
(=> (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 9114-9122	If an entity is an instance of leap year and the entity is an instance of the year an integer, then equal the integer mod 4 and 0 and equal not the integer mod 100 and 0 or equal the integer mod 400 and 0
(=> (and (not (equal ?NUMBER2 0)) (equal (AdditionFn (MultiplicationFn (FloorFn (DivisionFn ?NUMBER1 ?NUMBER2)) ?NUMBER2) ?NUMBER) ?NUMBER1)) (equal (RemainderFn ?NUMBER1 ?NUMBER2) ?NUMBER))	Merge.kif 5145-5156	If equal an integer and 0 and equal (the largest integer less than or equal to another integer and the integer and the integer and a third integer) and the other integer, then equal the other integer mod the integer and the third integer
(=> (instance ?NUMBER EvenInteger) (equal (RemainderFn ?NUMBER 2) 0))	Merge.kif 5172-5175	If an integer is an instance of even integer, then equal the integer mod 2 and 0
(=> (instance ?NUMBER OddInteger) (equal (RemainderFn ?NUMBER 2) 1))	Merge.kif 5177-5180	If an integer is an instance of odd integer, then equal the integer mod 2 and 1
(=> (instance ?PRIME PrimeNumber) (forall (?NUMBER) (=> (and (equal (RemainderFn ?PRIME ?NUMBER) 0) (not (equal ?NUMBER 0))) (or (equal ?NUMBER 1) (equal ?NUMBER ?PRIME)))))	Merge.kif 5182-5193	If an integer is an instance of prime number, then for all another integer if equal the integer mod the other integer and 0 and equal the other integer and 0, then equal the other integer and 1 or equal the other integer and the integer

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