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Proof step 23 from proof inv-rename-file-negdentry (previous step)

# links(entries0[str], dirs) = files[entries0[str]].nlink, # links(m0, dirs) = dirs[m0].nlink, # links(m, dirs) = dirs[m].nlink, entries0[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md4, dirs[m].nlink, dirs[m].nsubdirs, entries0), files[entries0[str]] = mkfile(m1, md2, files[entries0[str]].nlink, content), dirs[m0] = mkdir(dirs[m0].size, md3, dirs[m0].nlink, dirs[m0].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(entries0[str], md, false, files[entries0[str]].nlink, 0, m2), old_dent = mkdentry(str, entries0[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, str ∈ entries0, m ∈ dirs, entries0[str] ∈ files, m0 ∈ dirs, ¬ str0 ∈ dirs[m0].entries, ¬ str0 ∈ entries, m0 = m → md1 = md0, asynced → synced(files, icache, pcache), 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); 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) ∧ 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 24:
# links(m, dirs) = dirs[m].nlink, # links(m0, dirs) = dirs[m0].nlink, # links(entries0[str], dirs) = m4, dirs[m0] = mkdir(dirs[m0].size, md3, dirs[m0].nlink, dirs[m0].nsubdirs, entries), files[entries0[str]] = mkfile(m1, md2, m4, content), dirs[m] = mkdir(dirs[m].size, md4, dirs[m].nlink, dirs[m].nsubdirs, entries0), entries0[str] = dirs[m].entries[str], files[entries0[str]] = mkfile(m3, md5, m4, content0), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), old_child_inode = mkinode(entries0[str], md, false, m4, 0, m2), old_dent = mkdentry(str, entries0[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, entries0[str] ∈ files, m ∈ dirs, str ∈ entries0, str ∈ dirs[m].entries, asynced → synced(files, icache, pcache), m0 = m → md1 = md0, 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); 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) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))), str0 ∈ dirs[m0].entries, str0 ∈ entries

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[entries0[str]], m3, md5, m4, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[entries0[str]], m3, md5, m4, content0