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Proof step 18 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, (ino = m ⊃ files[m].content:= files[m].content[pageno, buf];mkfile(m0, md, m1, content)) = mkfile(m2, md0, m3, content0), files[ino] = mkfile(m0, md, m1, content), dirs[ino] = mkdir(m4, md1, m5, m6, entries), ino = m, afs-cons(dirs, files), m ∈ files, ROOT_INO ∈ dirs, ino ∈ dirs → m5 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m4 = # entries ∧ m6 = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# buf = VFS_PAGE_SIZE, dirs[m] = mkdir(m4, md1, m5, m6, entries), files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), n ∈ content[pageno, buf], ROOT_INO ∈ dirs, m ∈ files ⊦ # content[pageno, buf][n] = VFS_PAGE_SIZE, m ∈ dirs

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%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