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Proof step 12 from proof inv-link (previous step)

dirs[m] = mkdir(m0, md1, m1, m2, entries), c_inode = mkinode(dirs[ino].entries[str], md0, false, files[dirs[ino].entries[str]].nlink, 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, m1, m2, m0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), ino ∈ dirs, str ∈ dirs[ino].entries, m ∈ dirs, dirs[ino].entries[str] ∈ files, asynced → synced(files, icache, pcache), links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO ⊦ ⟪cache_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files)), str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
dirs[m] = mkdir(m0, md1, # links(m, dirs), m2, entries), c_inode = mkinode(dirs[ino].entries[str], md0, false, files[dirs[ino].entries[str]].nlink, 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), ino ∈ dirs, str ∈ dirs[ino].entries, m ∈ dirs, dirs[ino].entries[str] ∈ files, ¬ str0 ∈ entries, asynced → synced(files, icache, pcache), links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO ⊦ ⟪cache_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: 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