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

dirs[m0] = mkdir(m1, md2, # links(m0, dirs), m3, entries), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, # links(m0, dirs), m3, m1), old_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), old_dent = mkdentry(str, dirs[m].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), m0 ∈ dirs, m ∈ dirs, dirs[m].entries[str] ∈ dirs, str ∈ dirs[m].entries, ¬ str0 ∈ entries, asynced → synced(files, icache, pcache), m0 = m → md1 = md0, 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)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
dirs[m0] = mkdir(m1, md2, # links(m0, dirs), m3, entries), dirs[dirs[m].entries[str]] = mkdir(m2, md3, m4, m5, entries0), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, # links(m0, dirs), m3, m1), old_child_inode = mkinode(dirs[m].entries[str], md, true, m4, m5, m2), old_dent = mkdentry(str, dirs[m].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, dirs[m].entries[str] ∈ dirs, m ∈ dirs, m0 ∈ dirs, m0 = m → md1 = md0, 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))), str0 ∈ entries

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]], m2, md3, 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[dirs[m].entries[str]], m2, md3, m4, m5, entries0