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Then (i) $M$ is $(m+1)$-solid and $(m+1)$-universal, $(m+1)$ condensation holds for $M$, and if $m\\geq 1$ then $M$ is super-Dodd-sound, a slight strengthening of Dodd-soundness. 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Then (i) $M$ is $(m+1)$-solid and $(m+1)$-universal, $(m+1)$ condensation holds for $M$, and if $m\\geq 1$ then $M$ is super-Dodd-sound, a slight strengthening of Dodd-soundness. 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