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Proof step 25 from proof inv-link (previous step)

dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), dirs[m] = mkdir(m1, md2, # links(m, dirs), m5, entries1), files[entries0[str]] = mkfile(m0, md4, # links(entries0[str], dirs), content0), entries0[str] = entries[str], dirs[ino0] = mkdir(m2, md1, m7, m8, entries), c_inode = mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, # links(m, dirs), m5, m1), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries0[str] ∈ files, m ∈ dirs, str ∈ entries0, ino ∈ dirs, ino0 ∈ dirs, str ∈ entries, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪afs_link#(mkdentry(str, entries0[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced0); if err = ESUCCESS then let asynced = false in {icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, new_dent.name, new_dent; err, dcache)}⟫ ( 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 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), dirs[m] = mkdir(m1, md2, # links(m, dirs), m5, entries1), files[entries[str]] = mkfile(m0, md4, # links(entries[str], dirs), content0), entries0[str] = entries[str], dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), c_inode = mkinode(entries[str], md0, false, # links(entries[str], dirs), 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, # links(m, dirs), m5, 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, m ∈ dirs, str ∈ entries0, ino ∈ dirs, ino0 ∈ dirs, str ∈ entries, ¬ str0 ∈ entries1, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪afs_link#(mkdentry(str, entries0[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced0); if err = ESUCCESS then let asynced = false in {icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, new_dent.name, new_dent; err, dcache)}⟫ ( 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