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Proof step 28 from proof crash-neutral-rmdir (previous step)

dirs[entries0[str]] = mkdir(m3, md1, # links(entries0[str], dirs), m2, ∅), dirs[m] = mkdir(m0, md3, # links(m, dirs), m4, entries0), dirs1 = dirs[m, mkdir(m0 - 1, md3, # links(m, dirs), m4 - 1, entries0 -- str)], files0 = files, entries0[str] ≠ ROOT_INO, m0 ≠ 0, m4 ≠ 0, afs-cons(dirs, files), m ∈ dirs, entries0[str] ∈ dirs, str ∈ entries0, 1 ≤ m0, 1 ≤ m4, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs1, files); dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs), m4, m0); dirs1, files); afs_inode_sync#(mkinode(entries0[str], md2, true, # links(entries0[str], dirs), m2, m3); dirs1, files); p_inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (entries0[str] ∈ dirs1 ⊃ mkinode(entries0[str], dirs1[entries0[str]].meta, true, dirs1[entries0[str]].nlink, dirs1[entries0[str]].nsubdirs, dirs1[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs \ orphans(dirs, files0) = dirs1 \ orphans(dirs1, files) ∧ files0 \ orphans(dirs, files0) = files \ orphans(dirs1, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 29:
dirs0[m] = mkdir(m0, md3, # links(m, dirs0), m4, entries0), dirs0[entries0[str]] = mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅), dirs = dirs1, dirs1 = dirs0[m, mkdir(m0 - 1, md3, # links(m, dirs0), m4 - 1, entries0 -- str)], files0 = files, ino = mkdentry(str, entries0[str]).ino, mkdentry(str, entries0[str]).dentry?, afs-cons(dirs0, files), str ∈ entries0, entries0[str] ∈ dirs0, m ∈ dirs0, 1 ≤ m4, 1 ≤ m0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨if ino ∈ dirs then dirs[ino].nlink := dirs[ino].nlink - 1; if ino ∈ files then files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m4, m0); dirs, files); afs_inode_sync#(mkinode(entries0[str], md2, true, # links(entries0[str], dirs0), m2, m3); dirs, files); p_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) ); c_inode := (entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files0) = dirs \ orphans(dirs, files) ∧ files0 \ orphans(dirs0, files0) = files \ orphans(dirs, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced, entries0[str] = ROOT_INO, m0 = 0, m4 = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: drop-nlink: ⊦ ;% ⊦ mkdentry(str, m).dentry?; (s)