Given a sequentially Cauchy complete Archimedean ordered field$\mathbb{R}$, a function $f:\mathbb{R} \to \mathbb{R}$ is strongly extensional if for every $x:\mathbb{R}$ and $y:\mathbb{R}$, $\vert f(x) - f(y) \vert \gt 0$ implies that $\vert x - y \vert \gt 0$.

In particular, this definition applies to Dedekind real numbers, which is used for proving Brouwer's theorem? in real-cohesive homotopy type theory.