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Theorem subdirs-alloc

⊦ ¬ ino ∈ dirs ∧ ino ≠ 0 ∧ p_ino ∈ dirs ∧ ¬ ino ∈ dirs[p_ino].entries → subdirs(p_ino, dirs ++ ino) = subdirs(p_ino, dirs)

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