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Given a sequentially Cauchy complete Archimedean ordered field $\mathbb{R}$ and a function $f:\mathbb{R} \to \mathbb{R}$, the type of antiderivatives of $f$ is the fiber of the Newton-Leibniz operator at $f$:

$antiderivatives(f) \coloneqq \sum_{g:D^1(\mathbb{R}, \mathbb{R})} \tilde{D}(g) = f$

An **antiderivative** is a term of the above type.