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Fungrim entry: 7638c5

(d∣a and⁡ d∣b)  ⟹  (d∣gcd⁡ ⁣(a,b))\left(d \mid a \,\mathbin{\operatorname{and}}\, d \mid b\right) \implies \left(d \mid \gcd\!\left(a, b\right)\right)
Assumptions:a∈Z and⁡ b∈Z and⁡ d∈Za \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, d \in \mathbb{Z}
TeX:
\left(d \mid a \,\mathbin{\operatorname{and}}\, d \mid b\right) \implies \left(d \mid \gcd\!\left(a, b\right)\right)

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, d \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
GCDgcd⁡ ⁣(n,k)\gcd\!\left(n, k\right) Greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("7638c5"),
    Formula(Implies(And(Divides(d, a), Divides(d, b)), Divides(d, GCD(a, b)))),
    Variables(a, b, d),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(d, ZZ))))

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2019-06-18 07:49:59.356594 UTC