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Proof step 100 from proof refine-readdir (previous step)

root[path] = dnode(md, sdt), ((ino1 => mkdir(# entries, md, # links(ino1, dirs), m1, entries) * abs(sdt, entries) * abs|(root, ROOT_INO, path, ino1)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), path ∈ root, psynced → asynced ⊦ str ∈ entries ↔ str ∈ sdt

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%entries-dom2: ⊦ str ∈ sdt ∧ ((abs(sdt, sdi) * D))(dirs) → str ∈ sdi; (forward) from specification vfs-abs%entries-dom1: ⊦ str ∈ sdi ∧ ((abs(sdt, sdi) * D))(dirs) → str ∈ sdt; (forward) from specification vfs-abs