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Proof step 543 from proof inv-write (previous step)

dirs[ino] = mkdir(m7, md3, m8, m9, entries), of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), files[m] = mkfile(m2, md0, # links(m, dirs), content), files0[ino] = mkfile(m3, md1, m4, content1), files[ino] = mkfile(m5, md2, m6, content2), m1 < m0 + ino4, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons(of, dirs, files), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, m ∈ files, ROOT_INO ∈ dirs, n ≤ # buf0, ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files0, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs), ino ∈ dirs → m8 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m7 = # entries ∧ m9 = # subdirs(ino, dirs) ⊦ ino = m, ino4 = 0, n = 0, err1 = ESUCCESS ∧ ¬ isdir, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, (ino ∈ files → ¬ ino ∈ dirs ∧ m6 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: ino ∈ dirs

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss) Used formulas: ino ∈ dirs