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Proof step 15 from proof inv-rename-dir-dentry (previous step)

dirs[dirs[m].entries[str]].entries = ∅, new_child_inode = mkinode(dirs[m].entries[str], md, true, dirs[dirs[m].entries[str]].nlink, dirs[dirs[m].entries[str]].nsubdirs, dirs[dirs[m].entries[str]].size), new_dent = mkdentry(str, dirs[m].entries[str]), new_parent_inode = mkinode(m, md1, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode (dirs[m0].entries[str0], md0, true, dirs[dirs[m0].entries[str0]].nlink, dirs[dirs[m0].entries[str0]].nsubdirs, dirs[dirs[m0].entries[str0]].size), old_dent = mkdentry(str0, dirs[m0].entries[str0]), old_parent_inode = mkinode(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), dirs[m].entries[str] ≠ ROOT_INO, 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, str0 ∈ dirs[m0].entries, dirs[m].entries[str] ∈ dirs, dirs[m0].entries[str0] ∈ dirs, m ∈ dirs, m0 ∈ dirs, m = m0 → md1 = md2, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(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 16:
dirs[dirs[m].entries[str]] = mkdir(m1, md3, m2, m3, entries), entries = ∅, new_child_inode = mkinode(dirs[m].entries[str], md, true, m2, m3, m1), new_dent = mkdentry(str, dirs[m].entries[str]), new_parent_inode = mkinode(m, md1, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode (dirs[m0].entries[str0], md0, true, dirs[dirs[m0].entries[str0]].nlink, dirs[dirs[m0].entries[str0]].nsubdirs, dirs[dirs[m0].entries[str0]].size), old_dent = mkdentry(str0, dirs[m0].entries[str0]), old_parent_inode = mkinode(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m0 ∈ dirs, m ∈ dirs, dirs[m0].entries[str0] ∈ dirs, dirs[m].entries[str] ∈ dirs, str0 ∈ dirs[m0].entries, str ∈ dirs[m].entries, asynced → synced(files, icache, pcache), m = m0 → md1 = md2, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))), dirs[m].entries[str] = ROOT_INO

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[dirs[m].entries[str]], m1, md3, m2, m3, entries]

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[dirs[m].entries[str]], m1, md3, m2, m3, entries