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Proof step 40 from proof path-unfold (previous step)

((abs(sdt[str], entries[str]) * D * ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt -- str, entries -- str)))(dirs), (( ( ((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, ∀ 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), mkdir(# entries, md, m0, m1, entries).meta = md ∧ mkdir(# entries, md, m0, m1, entries).size = # mkdir(# entries, md, m0, m1, entries).entries ∧ (((ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt, mkdir(# entries, md, m0, m1, entries).entries)) * D))(dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
(( ( ((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) ⊦ (((ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt, entries)) * 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: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)