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Proof step 541 from proof inv-write (previous step)

(ino = m ⊃ mkfile(m0 + ino4, md, # links(m, dirs), content);files[ino]) = mkfile(m5, md2, m6, content2), 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), 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) ⊦ ino4 = 0, n = 0, (ino ∈ files → ¬ ino ∈ dirs ∧ m6 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files) ∧ (ino ∈ files ∧ n0 ∈ content2 → # content2[n0] = VFS_PAGE_SIZE), err1 = ESUCCESS ∧ ¬ isdir, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 542:
(ino = m ⊃ mkfile(m0 + ino4, md, # links(m, dirs), content);files[ino]) = mkfile(m5, md2, m6, content2), files0[ino] = mkfile(m3, md1, m4, content1), files[m] = mkfile(m2, md0, # links(m, dirs), content), files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dirs[ino] = mkdir(m7, md3, m8, m9, entries), dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), ROOT_INO ∈ dirs, m ∈ files, fd ∈ of, m ∈ files0, n ≤ # buf0, ino ∈ dirs → m8 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m7 = # entries ∧ m9 = # subdirs(ino, dirs), ino ∈ files0 → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files0 ⊦ ino = m, ino4 = 0, n = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, err1 = ESUCCESS ∧ ¬ isdir, (ino ∈ files → ¬ ino ∈ dirs ∧ m6 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files) ∧ (ino ∈ files ∧ n0 ∈ content2 → # content2[n0] = VFS_PAGE_SIZE)

Rule argument

fma: ino = m

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%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 ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s) Used formulas: ino = m