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Theorem links-add-entry

⊦ p_ino ∈ dirs → links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])]) = (ino = ino0 ⊃ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) ++ mklink(p_ino, str) ;(str ∈ entries ∧ entries[str] = ino0 ⊃ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) -- mklink(p_ino, str) ;links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) ) )

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