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Proof step 145 from proof refine-mkdir (previous step)

# links(ino1, dirs0) = m0, dirs0[ino1] = mkdir(# entries0, md1, # links(ino1, dirs0), m1, entries0), dent = negdentry(str), err = ESUCCESS, p_ino = ino1, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), ino1 ∈ dirs0, dirs4 ≡ dirs3 ++ ino, dirs2 ≡ dirs1[p_ino, dirs1[p_ino].size:= (dirs1[p_ino].size + 1)], dirs1 ≡ dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]], dirs3 ≡ dirs2[p_ino, dirs2[p_ino].nsubdirs:= (dirs2[p_ino].nsubdirs + 1)], dirs ≡ dirs4[ino, mkdir(0, md, 1, 0, ∅)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [dent := mkdentry(dent.name, ino); err := ESUCCESS; files0 := files; afs_inode_sync#(mkinode(ino1, md1, true, m0, m1, # entries0); dirs, files); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_mkdir#(q + str ', md, user, abs-files(files0), abs-of(of); err2, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), ino = 0, str ∈ entries0, ino ∈ files, ino ∈ dirs0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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