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Proof step 34 from proof absc-drop (previous step)

((((abs|(sdt[str0], entries[str0], q0, ino1) * abs(sdt -- str0, entries -- str0)) * ino0 => mkdir(# entries, md, m0, m1, entries)) * D))(dirs), sdt[str0][parent(p0)].dir?, parent(p0) ∈ sdt[str0], str0 ∈ sdt, str0 ∈ entries, q0 ⊑ p0, sdt[str0][parent(p0)].dir? ∧ parent(p0) ∈ sdt[str0] ∧ q0 ⊑ p0 → ( (( abs|(sdt[str0][p0, tree0], entries[str0], q0, ino1) * D * ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt -- str0, entries -- str0)) )(dirs) ↔ ((abs|(sdt[str0], entries[str0], q0, ino1) * D * ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt -- str0, entries -- str0)) )(dirs)) ∨ p0 = 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
((((abs|(sdt[str0], entries[str0], q0, ino1) * abs(sdt -- str0, entries -- str0)) * ino0 => mkdir(# entries, md, m0, m1, entries)) * D))(dirs), ((abs|(sdt[str0][p0, tree0], entries[str0], q0, ino1) * D * ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt -- str0, entries -- str0)) )(dirs), sdt[str0][parent(p0)].dir?, str0 ∈ entries, str0 ∈ sdt, parent(p0) ∈ sdt[str0], q0 ⊑ p0 ⊦ 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

Additional information

Used simplifier rules: eq-objs: ⊦ ((ino => ad * D))(dirs) ∧ ((ino => ad0 * D0))(dirs) → ad = ad0; (forward) from specification maplet[dir-heap]%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]