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Inverting Right Continuous Inverses does not decrease

Last updated Nov 1, 2022

# Statement

Suppose $F: \mathbb{R} \to \mathbb{R}$ is a Distribution Function and denote $F^{\rightarrow}$ to be its Right Continuous Inverse. Then $\forall x \in \mathbb{R}$:

$$F(F^{\rightarrow}(x)) \geq x$$

# Proof

TODO