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Proof step 22 from proof path-unfold (previous step)

(((ino0 => mkdir(# entries, md, m0, m1, entries) * (⌜str ∈ entries⌝ ∧ abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str]))) * D) )(dirs), str ∈ entries, p0 ∈ sdt[str], str ∈ sdt, ∀ tree, ino0, D, dirs. ((abs(tree, ino0) * D))(dirs) ∧ p0 ∈ tree → (∃ ino. (((abs|(tree, ino0, p0, ino) * abs(tree[p0], ino)) * D))(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 23:
((ino0 => mkdir(# entries, md, m0, m1, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * D))(dirs), str ∈ sdt, p0 ∈ sdt[str], str ∈ entries, ∀ tree, ino0, D, dirs. ((abs(tree, ino0) * D))(dirs) ∧ p0 ∈ tree → (∃ ino. (((abs|(tree, ino0, p0, ino) * abs(tree[p0], ino)) * D))(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)

Rule argument

Additional information

Used simplifier rules: and-com: ⊦ (D ∧ D0) = (D0 ∧ D); from specification heap-sep[dir-heap]%and-ass: ⊦ ((D ∧ D0) ∧ D1) = (D ∧ D0 ∧ D1); from specification heap-sep[dir-heap]% ⊦ (true ∧ D) = D; (s)% ⊦ ⌜true⌝ = true; (s)