## Definition ## The analytic Markov's principle states that for all points $x$ in the space of real numbers, if $x \leq 0$ is false, then $x \gt 0$. $$\prod_{x:\mathbb{R}} ((x \leq 0) \to \emptyset) \to (x \gt 0)$$ ## See also ## * [[axiom R-flat]] * [[intermediate value theorem]] ## References ## * [[Mike Shulman]], Brouwer’s fixed-point theorem in real-cohesive homotopy type theory, Mathematical Structures in Computer Science Vol 28 (6) (2018): 856-941 ([arXiv:1509.07584](https://arxiv.org/abs/1509.07584), [doi:10.1017/S0960129517000147](https://doi.org/10.1017/S0960129517000147))