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Proof step 37 from proof inv-rename-file-negdentry (previous step)

# links(m, dirs) = m6, dirs[m] = mkdir(m4, md3, m6, m7, entries), files[entries[str]] = mkfile(m1, md4, # links(entries[str], dirs), content), dirs[m0] = mkdir(m3, md5, # links(m0, dirs), m5, entries0), entries[str] = entries1[str], dirs[m] = mkdir(m4, md2, m6, m7, entries1), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, # links(m0, dirs), 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, m6, m7, m4), 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 ∈ entries1, 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 ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
dirs[m0] = mkdir(m3, md5, # links(m0, dirs), m5, entries0), files[entries1[str]] = mkfile(m1, md4, # links(entries1[str], dirs), content), dirs[m] = mkdir(m4, md2, # links(m, dirs), m7, entries1), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, # links(m0, dirs), m5, m3), old_child_inode = mkinode(entries1[str], md, false, # links(entries1[str], dirs), 0, m2), old_dent = mkdentry(str, entries1[str]), old_parent_inode = mkinode(m, md0, true, # links(m, dirs), m7, m4), 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, entries1[str] ∈ files, m ∈ dirs, str ∈ entries1, ¬ str0 ∈ entries0, 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))))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)