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Proof step 393 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries[str], dirs) = dirs[entries[str]].nlink, # links(m0, dirs) = m2, # links(m, dirs) = dirs[m].nlink, # links(entries1[str0], dirs) = dirs[entries1[str0]].nlink, dirs[entries[str]].entries = ∅, dirs[entries1[str0]] = mkdir(dirs[entries1[str0]].size, md5, dirs[entries1[str0]].nlink, dirs[entries1[str0]].nsubdirs, entries0), dirs[entries[str]] = mkdir(dirs[entries[str]].size, md3, dirs[entries[str]].nlink, dirs[entries[str]].nsubdirs, ∅), dirs[m] = mkdir(dirs[m].size, md4, dirs[m].nlink, dirs[m].nsubdirs, entries), dirs[m0] = mkdir(m1, md6, m2, m3, entries1), entries[str] = dirs[m].entries[str], entries1[str0] = entries2[str0], dirs[m0] = mkdir(m1, md, m2, m3, entries2), afs-cons(dirs, files), str ∈ entries, str0 ∈ entries1, entries[str] ∈ dirs, entries1[str0] ∈ dirs, m ∈ dirs, m0 ∈ dirs, str ∈ dirs[m].entries, str0 ∈ entries2, m = m0 → md1 = md2, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, entries[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 394:
# links(entries2[str0], dirs) = dirs[entries2[str0]].nlink, # links(m, dirs) = dirs[m].nlink, # links(entries[str], dirs) = dirs[entries[str]].nlink, dirs[entries[str]].entries = ∅, entries[str] = dirs[m].entries[str], dirs[m0] = mkdir(m1, md, # links(m0, dirs), m3, entries2), dirs[m] = mkdir(dirs[m].size, md4, dirs[m].nlink, dirs[m].nsubdirs, entries), dirs[entries[str]] = mkdir(dirs[entries[str]].size, md3, dirs[entries[str]].nlink, dirs[entries[str]].nsubdirs, ∅), dirs[entries2[str0]] = mkdir(dirs[entries2[str0]].size, md5, dirs[entries2[str0]].nlink, dirs[entries2[str0]].nsubdirs, entries0), entries[str] ≠ ROOT_INO, afs-cons(dirs, files), str ∈ dirs[m].entries, m0 ∈ dirs, m ∈ dirs, entries2[str0] ∈ dirs, entries[str] ∈ dirs, str0 ∈ entries2, str ∈ entries, m = m0 → md1 = md2, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base