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Proof step 87 from proof refine-mkdir (previous step)

dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, p_ino = ino1, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pre-lookup(p_ino, dent, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced ⊦ [ if dent.name ∈ dirs[p_ino].entries then {dent := mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT} or fail#(; ; err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; err1 := err; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {dent := negdentry((q + str ').last); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m1, # entries) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); afs_mkdir#(md; inode, c_inode, dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_mkdir#(q + str ', md, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0))

Heuristic conditional right split applied rule or split right

And obtained the following new goals

Rule argument

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