The binary expansion and the intermediate value theorem in constructive reverse mathematics

We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ($$\mathrm {BE}$$BE) is equivalent to weak König lemma ($$\mathrm {WKL}$$WKL) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to $$\mathrm {WKL}$$WKL for convex trees, in the framework of constructive reverse mathematics.

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