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Proof step 403 from proof inv-rename-dir-dentry (previous step)

dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs = dirs0, ino = inode.ino, inode = mkinode(m, md2, true, # links(m, dirs0), m4, m1), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m ∈ dirs0, entries0[str0] ∈ dirs0, str0 ∈ entries0, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta; afs_inode_sync#(mkinode(m, md2, true, # links(m, dirs0), m4, m1); dirs, files); new_child_inode := mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3); 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, entries0[str0]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[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)))), entries0[str0] = ROOT_INO

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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