The $\mathbb{Z}_p$-rank of the semilocal units $U_p(\mathbb{F})$ is at most $[\mathbb{F} : \mathbb{Q}]$

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The $\mathbb{Z}_p$-rank of the semilocal units $U_p(\mathbb{F})$ is at most $[\mathbb{F} : \mathbb{Q}]$ · Prove2Me