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We use this condition to show that given a set $\\mathcal{U}$ of distinguished joins from $P$, the lattice of $\\mathcal{U}$-ideals of $P$ fails to be a frame if and only if it fails to be $\\sigma$-distributive, with $\\sigma$ depending on the cardinalities of sets in $\\mathcal{U}$. 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We use this condition to show that given a set $\\mathcal{U}$ of distinguished joins from $P$, the lattice of $\\mathcal{U}$-ideals of $P$ fails to be a frame if and only if it fails to be $\\sigma$-distributive, with $\\sigma$ depending on the cardinalities of sets in $\\mathcal{U}$. 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