representing that the shape of $\mathbb{R}$ is contractible (which derives from axiom R-flat), and let $I$ be a closed interval or open interval in $\mathbb{R}$. Because the shape of $\mathbb{R}$ is contractible, the shape of any closed or open interval in $\mathbb{R}$ is contractible. Given a mapping $f:I \to \mathbb{R}$, let us define the graph $G$ of the mapping $f$ as

$G \coloneqq \sum_{x:I} (x, f(x))$

in the product type $I \times \mathbb{R}$. $f$ is continuous if the shape of $G$ is contractible: