Homotopy Type Theory antiderivative > history (Rev #4, changes)

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Definition

Given an a algebraic sequentially limit Cauchy complete Archimedean ordered field F F \mathbb{R} , and a functionsubtypef:f:\mathbb{R} \to \mathbb{R} , the type of antiderivatives of S fF S f \subseteq F , and is a the functionf:SFf:S \to F, the type of antiderivatives of ff is the fiber of the Newton-Leibniz operator at ff:

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

An antiderivative is a term of the above type.

See also

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