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

files[entries[str]] = mkfile(m0, md1, # links(entries[str], dirs), content), dirs[m] = mkdir(m1, md2, m2, m4, entries), c_inode = mkinode(entries[str], md0, false, # links(entries[str], dirs), 0, m3), dent = mkdentry(str, entries[str]), p_inode = mkinode(m, md, true, m2, m4, m1), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries[str] ∈ files, str ∈ entries, m ∈ dirs, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_unlink#(; p_inode, c_inode, 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
files[entries[str]] = mkfile(m0, md1, # links(entries[str], dirs), content), dirs[m] = mkdir(m1, md2, # links(m, dirs), m4, entries), c_inode = mkinode(entries[str], md0, false, # links(entries[str], dirs), 0, m3), dent = mkdentry(str, entries[str]), p_inode = mkinode(m, md, true, # links(m, dirs), m4, m1), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries[str] ∈ files, str ∈ entries, m ∈ dirs, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_unlink#(; p_inode, c_inode, 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