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Proof step 396 from proof inv-rename-dir-dentry (previous step)

# links(m, dirs0) = dirs0[m].nlink, # links(entries[str0], dirs0) = m1, entries[str0] = dirs0[m].entries[str0], entries1[str0] = entries[str0], dirs0[entries[str0]] = mkdir(m0, md3, m1, m2, entries2), dirs0[entries[str0]] = mkdir(m0, md6, m1, m2, ∅), dirs0[m] = mkdir(dirs0[m].size, md7, dirs0[m].nlink, dirs0[m].nsubdirs, entries1), dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs0[entries[str0]] = mkdir(m0, md0, m1, m2, entries0), dirs = dirs0[m, dirs0[m].entries:= (dirs0[m].entries -- str0).entries:= dirs0[m].entries], entries0 = ∅, afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), str0 ∈ dirs0[m].entries, str0 ∈ entries, entries[str0] ∈ dirs0, m ∈ dirs0, str0 ∈ entries1, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md2, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(m, md2, true, # links(m, dirs0), dirs0[m].nsubdirs, dirs0[m].size); dirs, files); new_child_inode := mkinode(entries1[str0], md, true, # links(entries1[str0], dirs0), dirs0[entries1[str0]].nsubdirs, dirs0[entries1[str0]].size); afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode(new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) ); old_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?] ( 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, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(mkdentry(str0, entries1[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries1[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))), entries[str0] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 397:
# links(m, dirs0) = dirs0[m].nlink, dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs0[m] = mkdir(dirs0[m].size, md7, dirs0[m].nlink, dirs0[m].nsubdirs, entries1), dirs0[entries[str0]] = mkdir(m0, md0, # links(entries[str0], dirs0), m2, ∅), entries1[str0] = entries[str0], entries[str0] = dirs0[m].entries[str0], dirs = dirs0[m, dirs0[m].entries:= (dirs0[m].entries -- str0).entries:= dirs0[m].entries], entries[str0] ≠ ROOT_INO, afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), str0 ∈ entries1, m ∈ dirs0, entries[str0] ∈ dirs0, str0 ∈ entries, str0 ∈ dirs0[m].entries, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md2, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(m, md2, true, # links(m, dirs0), dirs0[m].nsubdirs, dirs0[m].size); dirs, files); new_child_inode := mkinode(entries1[str0], md, true, # links(entries1[str0], dirs0), dirs0[entries1[str0]].nsubdirs, dirs0[entries1[str0]].size); afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode(new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) ); old_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?] ( 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, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(mkdentry(str0, entries1[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries1[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → 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)