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Fungrim entry: 96289e

∣atan⁡ ⁣(x+y)−atan⁡(x)∣≤∣y∣\left|\operatorname{atan}\!\left(x + y\right) - \operatorname{atan}(x)\right| \le \left|y\right|
Assumptions:x∈R  and⁡  y∈Rx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
TeX:
\left|\operatorname{atan}\!\left(x + y\right) - \operatorname{atan}(x)\right| \le \left|y\right|

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
Atanatan⁡(z)\operatorname{atan}(z) Inverse tangent
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("96289e"),
    Formula(LessEqual(Abs(Sub(Atan(Add(x, y)), Atan(x))), Abs(y))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

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2021-03-15 19:12:00.328586 UTC