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Proof step 455 from proof refine-unlink (previous step)

⟨vfs_put_inode#(getinode(entries0[str], dirs1, files), of, asynced; err3, dirs, files)⟩ (err3 = err2 ∧ dirs = dirs1 ∧ files = files1), # links(entries0[str], dirs0) = m + 1, # entries0 = m0 + 1, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), dirs = dirs1, err3 = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], fs = abs-files(files0), # links(ino1, dirs0) ≠ 0, entries0 ≠ ∅, ino1 ≠ ROOT_INO, links(ino1, dirs0) ≠ ∅, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs1, files1), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs1, files1), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), entries0[str] ∈ files0, str ∈ entries0, ino1 ∈ dirs0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs0, ¬ ino1 ∈ dirs1, ¬ entries0[str] ∈ dirs1, psynced → asynced0 ⊦ pre-unlink(q + str ', err2, user, root, fs, abs-of(of)) ∧ ⟨err0 := err2; if err0 = ESUCCESS then let fid = root[q + str '].fid in {root := root -- (q + str '); if ¬ fid ∈ abs-of(of).fids ∧ ¬ fid ∈ root.fids then fs := fs -- fid}; psynced := ?⟩ (root.dir? ∧ fids-cons(root, fs, abs-of(of)) → fs = abs-files(files1) ∧ abs(root, ROOT_INO)(dirs1) ∧ (psynced → asynced) ∧ err2 = err0)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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