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Theorem max0column-determines-clean1rows

c0 < #c mx, ∀ c. c < #c mx → ordered≤(mx[c]c), ∀ c. c < #c mx → count(mx[c]c, λ j. j < i) ≤ count(mx[c0]c, λ j. j < i) ⊦ #clean1rows(mx, i) + count(mx[c0]c, λ j. j < i) = #r mx

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