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Proof step 2 from proof expath-rec (previous step)

⊦ ispath(str ' + q, n, dirs, files) ↔ n ∈ dirs ∧ str ∈ dirs[n].entries ∧ ispath(q, dirs[n].entries[str], dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
dirs[n] = mkdir(m, md, m0, m1, entries) ⊦ ispath(str ' + q, n, dirs, files) ↔ n ∈ dirs ∧ str ∈ entries ∧ ispath(q, entries[str], 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, md, m, entries] → [dirs[n], md, m, 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[n], md, m, entries