An open problem solved

I proved the following (in)equalities, solving my open problem which stood for a few months:

\lvert \mathbb{R} \rvert_{>} \sqsubset \lvert \mathbb{R} \rvert_{\geq} \sqcap \mathord{>}

\lvert \mathbb{R} \rvert_{>} = \lvert \mathbb{R} \rvert_{>} \sqcap \mathord{>}

The proof is currently available in the section “Some inequalities” of this PDF file.

Note that earlier I put online some erroneous proof related to this.

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