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Proof step 9 from proof afs-cons-links-rmorphans (previous step)

dirs[m] = mkdir(m0, md, m1, m2, entries), afs-cons(dirs, files), m ∈ orphans(dirs, files), m ∈ dirs, str ∈ entries ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries), afs-cons(dirs, files), m ∈ orphans(dirs, files), m ∈ dirs, str ∈ entries ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n;