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Proof step 22 from proof inv-link (previous step)

# links(m, dirs) = dirs[m].nlink, entries0[str] = dirs[ino0].entries[str], files[entries0[str]] = mkfile(m0, md4, # links(entries0[str], dirs), content0), dirs[m] = mkdir(dirs[m].size, md1, dirs[m].nlink, dirs[m].nsubdirs, entries), dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), c_inode = mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ dirs[ino0].entries, ino0 ∈ dirs, ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries0[str] ∈ files, ¬ str0 ∈ entries, ¬ str0 ∈ dirs[m].entries, asynced → synced(files, icache, pcache), links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# links(m, dirs) = m2, dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), dirs[m] = mkdir(m1, md1, m2, m5, entries), files[entries0[str]] = mkfile(m0, md4, # links(entries0[str], dirs), content0), entries0[str] = dirs[ino0].entries[str], dirs[m] = mkdir(m1, md2, m2, m5, entries1), c_inode = mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, m2, 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 ∈ dirs[ino0].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 ∈ entries, str0 ∈ entries1

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[m], m1, md2, m2, m5, entries1]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m1, md2, m2, m5, entries1