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Proof step 50 from proof inv-rename-file-dentry (previous step)

# links(m, dirs) = m6, # links(m0, dirs) = dirs[m0].nlink, dirs[m] = mkdir(m1, md4, m6, m7, entries1), files[entries1[str]] = mkfile(m4, md6, # links(entries1[str], dirs), content0), files[entries[str0]] = mkfile(m5, md7, # links(entries[str0], dirs), content1), dirs[m0] = mkdir(dirs[m0].size, md5, dirs[m0].nlink, dirs[m0].nsubdirs, entries), entries1[str] = entries0[str], entries[str0] = dirs[m0].entries[str0], dirs[m] = mkdir(m1, md3, m6, m7, entries0), new_child_inode = mkinode(entries1[str], md, false, # links(entries1[str], dirs), 0, m2), new_dent = mkdentry(str, entries1[str]), new_parent_inode = mkinode(m, md1, true, m6, m7, m1), old_child_inode = mkinode(entries[str0], md0, false, # links(entries[str0], dirs), 0, m3), old_dent = mkdentry(str0, 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), str0 ∈ entries, m ∈ dirs, m0 ∈ dirs, entries1[str] ∈ files, entries[str0] ∈ files, str ∈ entries1, str ∈ entries0, str0 ∈ dirs[m0].entries, asynced → synced(files, icache, pcache), m = m0 → md1 = md2, 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); if true then icache_set#(new_child_inode, asynced; err, icache); 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)))), entries1[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
# links(m0, dirs) = dirs[m0].nlink, entries[str0] = dirs[m0].entries[str0], dirs[m0] = mkdir(dirs[m0].size, md5, dirs[m0].nlink, dirs[m0].nsubdirs, entries), files[entries[str0]] = mkfile(m5, md7, # links(entries[str0], dirs), content1), files[entries0[str]] = mkfile(m4, md6, # links(entries0[str], dirs), content0), dirs[m] = mkdir(m1, md3, # links(m, dirs), m7, entries0), new_child_inode = mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m2), new_dent = mkdentry(str, entries0[str]), new_parent_inode = mkinode(m, md1, true, # links(m, dirs), m7, m1), old_child_inode = mkinode(entries[str0], md0, false, # links(entries[str0], dirs), 0, m3), old_dent = mkdentry(str0, 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), str0 ∈ dirs[m0].entries, str ∈ entries0, entries[str0] ∈ files, entries0[str] ∈ files, m0 ∈ dirs, m ∈ dirs, str0 ∈ entries, ¬ entries0[str] ∈ dirs, m = m0 → md1 = md2, 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); if true then icache_set#(new_child_inode, asynced; err, icache); 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)