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Fungrim entry: f91d1c

gcd⁡ ⁣(a,b)≤min⁡ ⁣(∣a∣,∣b∣)\gcd\!\left(a, b\right) \le \min\!\left(\left|a\right|, \left|b\right|\right)
Assumptions:a∈Z∖{0}  and⁡  b∈Z∖{0}a \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \setminus \left\{0\right\}
TeX:
\gcd\!\left(a, b\right) \le \min\!\left(\left|a\right|, \left|b\right|\right)

a \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
GCDgcd⁡ ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Abs∣z∣\left|z\right| Absolute value
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("f91d1c"),
    Formula(LessEqual(GCD(a, b), Min(Abs(a), Abs(b)))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, SetMinus(ZZ, Set(0))))))

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2021-03-15 19:12:00.328586 UTC