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Proof step 537 from proof inv-write (previous step)

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 ∈ files0 ∧ n0 ∈ content1 → # content1[n0] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs) ⊦ ino4 = 0, n = 0, (ino ∈ files → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m0 + ino4, md, # links(m, dirs), content);files[ino]).nlink = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ ( ino ∈ files ∧ n0 ∈ (ino = m ⊃ mkfile(m0 + ino4, md, # links(m, dirs), content);files[ino]).content → # (ino = m ⊃ mkfile(m0 + ino4, md, # links(m, dirs), content);files[ino]).content[n0] = VFS_PAGE_SIZE), err1 = ESUCCESS ∧ ¬ isdir, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 538:
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), 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 ∈ files0 → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0 ⊦ 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 ∧ (ino = m ⊃ mkfile(m0 + ino4, md, # links(m, dirs), content);files[ino]).nlink = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ ( ino ∈ files ∧ n0 ∈ (ino = m ⊃ mkfile(m0 + ino4, md, # links(m, dirs), content);files[ino]).content → # (ino = m ⊃ mkfile(m0 + ino4, md, # links(m, dirs), content);files[ino]).content[n0] = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)