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Proof step 24 from proof path-unfold (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
((ino0 => mkdir(# entries, md, m0, m1, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * D))(dirs), (( (abs|(sdt[str], entries[str], p0, ino) * abs(sdt[str][p0], ino)) * D * abs(sdt -- str, entries -- str) * ino0 => mkdir(# entries, md, m0, m1, entries)) )(dirs), str ∈ sdt, p0 ∈ sdt[str], str ∈ entries ⊦ ∃ ino, ad0. str ∈ ad0.entries ∧ ad0.meta = md ∧ ad0.size = # ad0.entries ∧ (((((abs|(sdt[str], ad0.entries[str], p0, ino) * abs(sdt -- str, ad0.entries -- str)) * ino0 => ad0) * abs(sdt[str][p0], ino)) * 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]