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Proof step 1 from proof dir-empty (conclusion)

⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ dirs ∧ dirs[m] = mkdir(m0, md, n0, n1, entries) ∧ str ∈ entries ∧ entries[str] ∈ dirs → (dirs[entries[str]].entries = ∅ ↔ tree[p + str '].entries = ∅)

System applied rule normalize

And obtained the following new goals

Proof step 2:
dirs[m] = mkdir(m0, md, n0, n1, entries), abs(tree, ino)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ino, m, dirs, files), px-parent(user, p, ino, dirs, files), m ∈ dirs, str ∈ entries, entries[str] ∈ dirs ⊦ dirs[entries[str]].entries = ∅ ↔ tree[p + str '].entries = ∅

Proof step 1 from proof dir-empty (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information