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Proof step 96 from proof refine-readdir (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root[path] = dnode(md0, sdt), ((abs|(root, ROOT_INO, path, ino1) * _∃(λ ad. ino1 => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md0⌝ ∧ ⌜ad.size = # ad.entries⌝ )))(dirs), root.dir?, dom of < ino0, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), path ∈ root, ino1 ∈ dirs, psynced → asynced ⊦ dom entries = dom sdt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
root[path] = dnode(md, sdt), ((ino1 => mkdir(# entries, md, # links(ino1, dirs), m1, entries) * abs(sdt, entries) * abs|(root, ROOT_INO, path, ino1)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), path ∈ root, psynced → asynced ⊦ dom entries = dom sdt

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)% ⊦ ((ino => ad * D))(dirs) → ino ∈ dirs; (s)% ⊦ ((ino => ad * D))(dirs) → (dirs[ino] = ad0 ↔ ad = ad0); (s)% ⊦ ⌜bv⌝ (dirs) ↔ bv; (s)% ⊦ ((D ∧ D0))(dirs) ↔ D(dirs) ∧ D0(dirs); (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]%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]% ⊦ (⌜bv⌝ ∧ D) * D0 = (⌜bv⌝ ∧ D * D0); (s)% ⊦ ((_∃ adD * D))(dirs) ↔ (∃ ad. ((adD(ad) * D))(dirs)); (s)