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Proof step 22 from proof crash-neutral-unlink (previous step)

# links(m, dirs) = m1, c_inode.ino = entries[str], c_inode.nlink = files[entries[str]].nlink, c_inode.nsubdirs = 0, dirs[m] = mkdir(m0, md0, m1, m2, entries), entries[str] = entries0[str], dirs[m] = mkdir(m0, md1, m1, m2, entries0), dirs1 = dirs[m, (dirs[m].entries:= (entries0 -- str)).size:= (m0 - 1)], files0 = files, afs-cons(dirs, files), m ∈ dirs, entries[str] ∈ files, str ∈ entries0, str ∈ entries, 1 ≤ m0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs1, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, m1, m2, m0); dirs1, files); afs_inode_sync#(c_inode; 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 := (c_inode.ino ∈ dirs1 ⊃ mkinode(c_inode.ino, dirs1[c_inode.ino].meta, true, dirs1[c_inode.ino].nlink, dirs1[c_inode.ino].nsubdirs, dirs1[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].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, m0 = 0, c_inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
c_inode.ino = entries0[str], c_inode.nlink = files[entries0[str]].nlink, c_inode.nsubdirs = 0, dirs[m] = mkdir(m0, md1, # links(m, dirs), m2, entries0), dirs1 = dirs[m, mkdir(m0 - 1, md1, # links(m, dirs), m2, entries0 -- str)], files0 = files, m0 ≠ 0, afs-cons(dirs, files), str ∈ entries0, entries0[str] ∈ files, m ∈ dirs, 1 ≤ m0, ¬ c_inode.directory, 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), m2, m0); dirs1, files); afs_inode_sync#(c_inode; 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 := (c_inode.ino ∈ dirs1 ⊃ mkinode(c_inode.ino, dirs1[c_inode.ino].meta, true, dirs1[c_inode.ino].nlink, dirs1[c_inode.ino].nsubdirs, dirs1[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].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

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat