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Proof step 41 from proof abs-nlinks-h (previous step)

tree[p0 + str '] = fnode(⌜ino1⌝ ), tree[p0] = dnode(md, sdt), dirs[m0] = mkdir(m, md0, m3, m4, entries0), ((m0 => mkdir(# entries, md, m1, m2, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * abs|(tree, ino0, p0, m0)) )(dirs), ispath(p0, ino0, m0, dirs, files), str ∈ entries, ino0 ∈ dirs, ino1 ∈ files, p0 ∈ tree, str ∈ sdt, ∀ alink. ¬ alink.pino ∈ dirs ∨ ¬ alink.name ∈ dirs[alink.pino].entries ∨ ino1 ≠ dirs[alink.pino].entries[alink.name], ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ¬ str ∈ entries0 ∨ ino1 ≠ entries0[str], entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
tree[p0 + str '] = fnode(⌜ino1⌝ ), tree[p0] = dnode(md, sdt), ((m0 => mkdir(# entries0, md, m1, m2, entries0) * (abs(sdt -- str, entries0 -- str) * abs(sdt[str], entries0[str])) * abs|(tree, ino0, p0, m0)) )(dirs), ispath(p0, ino0, m0, dirs, files), str ∈ entries0, ino0 ∈ dirs, ino1 ∈ files, p0 ∈ tree, str ∈ sdt, ∀ alink. ¬ alink.pino ∈ dirs ∨ ¬ alink.name ∈ dirs[alink.pino].entries ∨ ino1 ≠ dirs[alink.pino].entries[alink.name], ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, entries0[str] ∈ dirs ∨ entries0[str] ∈ files ⊦ ino1 = entries0[str]

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ ((ino => ad * D))(dirs) → (dirs[ino] = ad0 ↔ ad = ad0); (s)%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]