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Proof step 18 from proof refine-link (previous step)

root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced, path = ε ∨ path' = ε ⊦ root[path'].dir?, root[path].dir?

User applied rule case distinction

And closed the goal!

Rule argument

pos: left 8

Additional information

Used simplifier rules: ⊦ tree[ε] = tree; (s)