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Theorem pre-write-inode

⊦ pre-write-inode(inode, fs, ri, ro) ↔ (valid-file-inode(inode, fs, ri) ∨ valid-dir-inode(inode, fs, ri)) ∧ (fs[ri[inodekey(inode.ino)]].nlink = 0 ∧ inode.ino ≠ ROOT_INO ↔ inodekey(inode.ino) ∈ ro)