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Proof step 6 from proof subdirs-delete-orphans (previous step)

dirs[ino].entries[str] ∈ dirs, str ∈ dirs[ino].entries, ino ∈ dirs, dirs[ino].entries[str] ∈ orphans(dirs, files) ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅, ino ∈ orphans(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
dirs[ino] = mkdir(m, md, m0, m1, entries), entries[str] ∈ orphans(dirs, files), ino ∈ dirs, str ∈ entries, entries[str] ∈ dirs ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅, ino ∈ 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, m1, entries] → [dirs[ino], m, md, m0, 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[ino], m, md, m0, m1, entries