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Proof step 8 from proof afs-cons-links-rmorphans (previous step)

afs-cons(dirs, files), str ∈ dirs[m].entries, m ∈ dirs, m ∈ orphans(dirs, files) ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
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) = ∅

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, entries] → [dirs[m], m0, md, m1, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m0, md, m1, entries