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Proof step 31 from proof absc-drop (previous step)

ad.size = # ad.entries, ((((abs|(sdt[str0], ad.entries[str0], q0, ino1) * abs(sdt -- str0, ad.entries -- str0)) * ino0 => ad) * D))(dirs), sdt[str0][parent(p0)].dir?, str0 ∈ ad.entries, str0 ∈ sdt, parent(p0) ∈ sdt[str0], q0 ⊑ p0, ∀ tree, p, tree0, ino0, ino1, D, dirs. tree[parent(p)].dir? ∧ parent(p) ∈ tree ∧ q0 ⊑ p → (((abs|(tree[p, tree0], ino0, q0, ino1) * D))(dirs) ↔ ((abs|(tree, ino0, q0, ino1) * D))(dirs)) ∨ p = ε ⊦ p0 = ε, ∃ ad0. str0 ∈ ad0.entries ∧ ad0.meta = ad.meta ∧ ad0.size = # ad0.entries ∧ ((((abs|(sdt[str0][p0, tree0], ad0.entries[str0], q0, ino1) * abs(sdt -- str0, ad0.entries -- str0)) * ino0 => ad0) * D))(dirs)

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, ((((abs|(sdt[str0], entries[str0], q0, ino1) * abs(sdt -- str0, entries -- str0)) * ino0 => ad) * D))(dirs), sdt[str0][parent(p0)].dir?, parent(p0) ∈ sdt[str0], str0 ∈ sdt, str0 ∈ entries, q0 ⊑ p0, ∀ tree, p, tree0, ino0, ino1, D, dirs. tree[parent(p)].dir? ∧ parent(p) ∈ tree ∧ q0 ⊑ p → (((abs|(tree[p, tree0], ino0, q0, ino1) * D))(dirs) ↔ ((abs|(tree, ino0, q0, ino1) * D))(dirs)) ∨ p = ε ⊦ p0 = ε, ∃ ad0. str0 ∈ ad0.entries ∧ ad0.meta = md ∧ ad0.size = # ad0.entries ∧ ((((abs|(sdt[str0][p0, tree0], ad0.entries[str0], q0, ino1) * abs(sdt -- str0, ad0.entries -- str0)) * ino0 => ad0) * 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, m1, entries] → [ad, m, md0, 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: ad, m, md0, m0, m1, entries