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Proof step 38 from proof path-unfold (previous step)

(( ( ((abs|(sdt[str], entries[str], p0, ino) * abs(sdt -- str, entries -- str)) * ino0 => mkdir(# entries, md, m0, m1, entries)) * abs(sdt[str][p0], ino)) * D) )(dirs), str ∈ sdt, p0 ∈ sdt[str], str ∈ entries, (( (abs|(sdt[str], entries[str], p0, ino) * abs(sdt[str][p0], ino)) * D * ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt -- str, entries -- str)) )(dirs) ∧ p0 ∈ sdt[str] → ((abs(sdt[str], entries[str]) * D * ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt -- str, entries -- str)))(dirs), ∀ 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
(( ( ((abs|(sdt[str], entries[str], p0, ino) * abs(sdt -- str, entries -- str)) * ino0 => mkdir(# entries, md, m0, m1, entries)) * abs(sdt[str][p0], ino)) * D) )(dirs), ((abs(sdt[str], entries[str]) * D * ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt -- str, entries -- str)))(dirs), str ∈ 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 = md ∧ ad0.size = # ad0.entries ∧ (((ino0 => ad0 * abs(sdt, ad0.entries)) * 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]