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Proof step 30 from proof afs-cons-rename-dir-negdentry (previous step)

asynced0 ↔ old_ino = new_ino ∧ new_dent = old_dent, asynced1 ↔ new_dent.dentry?, dirs0[m] = mkdir(m4, md4, # links(m, dirs0), m7, entries1), dirs0[m0] = mkdir(m1, md2, # links(m0, dirs0), m3, entries), dirs0[entries1[str]] = mkdir(m2, md3, # links(entries1[str], dirs0), m5, entries0), ¬ asynced0, dirs = dirs2[old_ino, dirs2[old_ino].nsubdirs:= (dirs2[old_ino].nsubdirs - 1)] [new_ino, dirs2[old_ino, dirs2[old_ino].nsubdirs:= (dirs2[old_ino].nsubdirs - 1)][new_ino] .entries:= dirs2[old_ino, dirs2[old_ino].nsubdirs:= (dirs2[old_ino].nsubdirs - 1)][new_ino].entries[new_dent.name, old_dent.ino] ], dirs1 = dirs0[old_ino, dirs0[old_ino].entries:= (dirs0[old_ino].entries -- old_dent.name)], dirs2 = dirs1[old_ino, dirs1[old_ino].size:= (dirs1[old_ino].size - 1)], new_dent = negdentry(str0), new_ino = new_parent_inode.ino, new_parent_inode = mkinode(m0, md1, true, # links(m0, dirs0), m3, m1), old_child_inode = mkinode(entries1[str], md, true, # links(entries1[str], dirs0), m5, m2), old_dent = mkdentry(str, entries1[str]), old_ino = old_parent_inode.ino, old_parent_inode = mkinode(m, md0, true, # links(m, dirs0), m7, m4), old_dent.dentry?, afs-cons(dirs0, files), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs0, files), old_dent.ino ∈ dirs2, str ∈ entries1, entries1[str] ∈ dirs0, m ∈ dirs0, m0 ∈ dirs0, dirs1[old_ino].size ≥ 1, dirs2[old_ino].nsubdirs ≥ 1, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ asynced1 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), str0 ∈ entries

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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