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Proof step 35 from proof path-unfold (previous step)

ad.size = # ad.entries, (((((abs|(sdt[str], ad.entries[str], p0, ino) * abs(sdt -- str, ad.entries -- str)) * ino0 => ad) * abs(sdt[str][p0], ino)) * D))(dirs), str ∈ ad.entries, p0 ∈ sdt[str], str ∈ sdt, ∀ tree, ino0, ino, D, dirs. (((abs|(tree, ino0, p0, ino) * abs(tree[p0], ino)) * D))(dirs) ∧ p0 ∈ tree → ((abs(tree, ino0) * D))(dirs) ⊦ ∃ ad0. ad0.meta = ad.meta ∧ ad0.size = # ad0.entries ∧ (((ino0 => ad0 * abs(sdt, ad0.entries)) * D))(dirs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 36:
ad = mkdir(m, md, m0, m1, entries), m = # entries, (((((abs|(sdt[str], entries[str], p0, ino) * abs(sdt -- str, entries -- str)) * ino0 => ad) * abs(sdt[str][p0], ino)) * D))(dirs), str ∈ sdt, p0 ∈ sdt[str], str ∈ entries, ∀ tree, ino0, ino, D, dirs. (((abs|(tree, ino0, p0, ino) * abs(tree[p0], ino)) * D))(dirs) ∧ p0 ∈ tree → ((abs(tree, ino0) * D))(dirs) ⊦ ∃ ad0. ad0.meta = md ∧ ad0.size = # ad0.entries ∧ (((ino0 => ad0 * abs(sdt, ad0.entries)) * D))(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