= Solution
Given observed data $x$, a <credible interval> $[L(x),U(x)]$ has posterior <probability> $1-\alpha$:
$$
\boxed{\Pr\{L(x)\leq\theta\leq U(x)\mid x\}=1-\alpha.}
$$
For a continuous <posterior distribution> with <probability density function> $\pi(\theta\mid x)$, this is $\int_{L(x)}^{U(x)}\pi(\theta\mid x)\,d\theta=1-\alpha$. The probability is conditional on the observed data and concerns the <statistical parameter> under its <posterior distribution>; it does not assert frequentist <coverage probability>.
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