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Proof step 139 from proof refine-mkdir (previous step)

# links(ino1, dirs) = m0, dirs[ino1] = mkdir(# entries0, md1, # links(ino1, dirs), m1, entries0), dent = negdentry(str), err = ESUCCESS, ino ≠ 0, root.dir?, root[q].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), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, ¬ ino ∈ dirs, ¬ ino ∈ files, ¬ str ∈ entries0, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_mkdir_ino#(ino1, md, ino; dent, err, dirs); 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))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 140:
# links(ino1, dirs) = m0, dirs[ino1] = mkdir(# entries0, md1, # links(ino1, dirs), m1, entries0), 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), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [dirs[p_ino].entries[dent.name] := ino; dirs[p_ino].size := dirs[p_ino].size + 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs + 1; dirs := dirs ++ ino; dirs[ino] := mkdir(0, md, 1, 0, ∅); 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, ino ∈ dirs, ino ∈ files, str ∈ entries0

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_mkdir_ino#(P_INO, MD, INO; DENT, ERR, DIRS) {DIRS[P_INO].entries[DENT.name] := INO; DIRS[P_INO].size := DIRS[P_INO].size + 1; DIRS[P_INO].nsubdirs := DIRS[P_INO].nsubdirs + 1; DIRS := DIRS ++ INO; DIRS[INO] := mkdir(0, MD, 1, 0, ∅); DENT := mkdentry(DENT.name, INO); ERR := ESUCCESS };