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Proof step 31 from proof abs-unshared-h (previous step)

ad.meta = tree0[p0].meta, ad.size = # ad.entries, ((((((n1 => ad * abs(tree0[p0].entries, ad.entries)) * abs|(tree1, ino1, p1, n1)) * abs(tree1[p1], n1)) * abs|(tree0, ino0, p0, n1)) * D))(dirs), tree0[p0].dir?, ispath(p0, ino0, n1, dirs, files), ispath(p1, ino1, n1, dirs, files), p0 ∈ tree0, p1 ∈ tree1, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
ad = mkdir(m, md, m0, m1, entries), m = # entries, md = tree0[p0].meta, ((((((n1 => ad * abs(tree0[p0].entries, entries)) * abs|(tree1, ino1, p1, n1)) * abs(tree1[p1], n1)) * abs|(tree0, ino0, p0, n1)) * D))(dirs), tree0[p0].dir?, ispath(p1, ino1, n1, dirs, files), ispath(p0, ino0, n1, dirs, files), p1 ∈ tree1, p0 ∈ tree0, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦

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] → [ad, m, md, m0, 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: ad, m, md, m0, entries