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KB Term:  Term intersection
English Word: 

  GreatestCommonDivisorFn

 Sigma KEE - GreatestCommonDivisorFn
GreatestCommonDivisorFn

appearance as argument number 1
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(instance GreatestCommonDivisorFn Function) Merge.kif 4956-4956 Greatest common divisor is an instance of function
(instance GreatestCommonDivisorFn VariableArityRelation) Merge.kif 4957-4957 Greatest common divisor is an instance of variable arity relation
(instance GreatestCommonDivisorFn PartialValuedRelation) Merge.kif 4958-4958 Greatest common divisor is an instance of partial valued relation
(range GreatestCommonDivisorFn Integer) Merge.kif 4959-4959 The range of greatest common divisor is an instance of integer
(domain GreatestCommonDivisorFn 1 Integer) Merge.kif 4960-4960 The number 1 argument of greatest common divisor is an instance of integer
(documentation GreatestCommonDivisorFn EnglishLanguage "(GreatestCommonDivisorFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the greatest common divisor of ?NUMBER1 through ?NUMBER.") Merge.kif 4962-4964 The number 1 argument of greatest common divisor is an instance of integer

appearance as argument number 2
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(termFormat EnglishLanguage GreatestCommonDivisorFn "greatest common divisor") domainEnglishFormat.kif 26546-26546
(termFormat ChineseTraditionalLanguage GreatestCommonDivisorFn "最大公約數") domainEnglishFormat.kif 26547-26547
(termFormat ChineseLanguage GreatestCommonDivisorFn "最大公约数") domainEnglishFormat.kif 26548-26548
(format EnglishLanguage GreatestCommonDivisorFn "the greatest common divisor of %*[and]") english_format.kif 702-702

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


(=>
    (equal
        (GreatestCommonDivisorFn @ROW) ?NUMBER)
    (=>
        (inList ?ELEMENT
            (ListFn @ROW))
        (instance ?ELEMENT Number)))		 Merge.kif 4966-4971 Assuming equal the greatest common divisor of @ROW and Y, it follows that: if Z is a member of (@ROW), then Z is an instance of number
(=>
    (and
        (equal
            (GreatestCommonDivisorFn @ROW) ?NUMBER)
        (not
            (equal ?NUMBER 0)))
    (forall (?ELEMENT)
        (=>
            (inList ?ELEMENT
                (ListFn @ROW))
            (equal
                (RemainderFn ?ELEMENT ?NUMBER) 0))))		 Merge.kif 4973-4984 If equal the greatest common divisor of @ROW and Y and equal Y and 0, then For all Integer Z: if Z is a member of (@ROW), then equal Z mod Y 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 4986-5000 If equal the greatest common divisor of @ROW and Y and equal Y and 0, then there doesn't exist Z such that Z is greater than Y and W W is a member of (@ROW)equal W mod Z and 0


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