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Proof step 86 from proof crash-neutral-rmdir (previous step)

# links(entries[str], dirs) = c_inode.nlink, # links(m, dirs) = dirs[m].nlink, c_inode.ino = entries[str], dirs[entries[str]] = mkdir(c_inode.size, md1, c_inode.nlink, c_inode.nsubdirs, ∅), dirs[m] = mkdir(dirs[m].size, md0, dirs[m].nlink, dirs[m].nsubdirs, entries), entries[str] = dirs[m].entries[str], p_ino = m, c_inode.directory, afs-cons(dirs, files), m ∈ dirs, str ∈ entries, entries[str] ∈ dirs, str ∈ dirs[m].entries, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- mkdentry(str, entries[str]).name)][p_ino].size ≥ 1, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- mkdentry(str, entries[str]).name)] [p_ino, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- mkdentry(str, entries[str]).name)][p_ino] .size:= (dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- mkdentry(str, entries[str]).name)][p_ino].size - 1) ] [p_ino ] .nsubdirs ≥ 1, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, entries[str] = ROOT_INO, mkdentry(str, entries[str]).dentry? ∧ str ∈ entries

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ (ad.entries:= entries).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.size:= m).nsubdirs = ad.nsubdirs; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)