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Proof step 18 from proof abs-unfold (previous step)

dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m1, entries), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), ino ∈ dirs, ∃ sdt. ((abs|(tree, ROOT_INO, p, ino) * ino => mkdir(# entries, md, # links(ino, dirs), m1, entries) * abs(sdt, entries)))(dirs) ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt) ⊦ abs(tree0, ROOT_INO)(dirs0), abs(tree, ROOT_INO)(dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
tree[p] = dnode(md, sdt), ((abs|(tree, ROOT_INO, p, ino) * ino => mkdir(# entries, md, # links(ino, dirs), m1, entries) * abs(sdt, entries)))(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), p ∈ tree ⊦ abs(tree, ROOT_INO)(dirs), abs(tree0, ROOT_INO)(dirs0)

Rule argument

Additional information

Used simplifier rules: ⊦ ((ino => ad * D))(dirs) → ino ∈ dirs; (s)% ⊦ ((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]