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Probably it can be done easier if you do both steps separately ($\implies$ and $\impliedby$), but here is a proof that does both at the same time: \begin{align*} &x\succ y \vee x\sim y\\ \iff\;& x \succ y \vee (x\succeq y \wedge y \succeq x) & \text{Definition of $\sim$} \\ \iff\;& (x \succ y \vee x\succeq y) \wedge (x \succ y \vee y \...


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