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Proof step 74 from proof crash-neutral-unlink (previous step)

# links(m, dirs) = dirs[m].nlink, c_inode.ino = entries[str], c_inode.nlink = files[entries[str]].nlink, c_inode.nsubdirs = 0, entries[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md0, dirs[m].nlink, dirs[m].nsubdirs, entries), p_ino = m, afs-cons(dirs, files), str ∈ dirs[m].entries, entries[str] ∈ files, str ∈ entries, m ∈ dirs, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- mkdentry(str, entries[str]).name)][p_ino].size ≥ 1, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, c_inode.directory, 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).size = ad.size; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)