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Proof step 34 from proof inv-rename-file-negdentry (previous step)

# links(m, dirs) = dirs[m].nlink, # links(m0, dirs) = dirs[m0].nlink, entries[str] = dirs[m].entries[str], dirs[m0] = mkdir(dirs[m0].size, md2, dirs[m0].nlink, dirs[m0].nsubdirs, entries1), files[entries[str]] = mkfile(m1, md4, # links(entries[str], dirs), content), dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), old_child_inode = mkinode(entries[str], md, false, # links(entries[str], dirs), 0, m2), old_dent = mkdentry(str, entries[str]), old_parent_inode = mkinode(m, md0, 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[m].entries, m0 ∈ dirs, entries[str] ∈ files, m ∈ dirs, str ∈ entries, ¬ str0 ∈ entries1, ¬ str0 ∈ dirs[m0].entries, m0 = m → md1 = md0, asynced → synced(files, icache, pcache), links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); skip; dcache_delete#(old_parent_inode.ino, old_dent.name; err, dcache); dcache_set#(new_parent_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))))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
# links(m0, dirs) = m4, # links(m, dirs) = dirs[m].nlink, dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries), files[entries[str]] = mkfile(m1, md4, # links(entries[str], dirs), content), dirs[m0] = mkdir(m3, md2, m4, m5, entries1), entries[str] = dirs[m].entries[str], dirs[m0] = mkdir(m3, md5, m4, m5, entries0), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, m4, m5, m3), old_child_inode = mkinode(entries[str], md, false, # links(entries[str], dirs), 0, m2), old_dent = mkdentry(str, entries[str]), old_parent_inode = mkinode(m, md0, 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 ∈ entries, m ∈ dirs, entries[str] ∈ files, m0 ∈ dirs, str ∈ dirs[m].entries, asynced → synced(files, icache, pcache), m0 = m → md1 = md0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ [afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); skip; dcache_delete#(old_parent_inode.ino, old_dent.name; err, dcache); dcache_set#(new_parent_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)))), str0 ∈ entries1, str0 ∈ entries0

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[m0], m3, md5, m4, m5, entries0]

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[m0], m3, md5, m4, m5, entries0