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Proof step 65 from proof refine-writemeta (previous step)

dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), err0 = ESUCCESS, fs = abs-files(files), root.dir?, root[path].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), m ∈ dirs0, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced0 → asynced0 ⊦ ∃ psynced. fs = abs-files(files) ∧ abs(root[path, root[path].meta:= md], ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
⊦ ispath(p, ROOT_INO, ino, dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, m0, m1, entries) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ ¬ abs(tree0, ROOT_INO)(dirs0) → ( abs(tree, ROOT_INO)(dirs) ↔ (∃ sdt. ((abs|(tree, ROOT_INO, p, ino) * ino => mkdir(n, md, m0, m1, entries) * abs(sdt, entries)))(dirs) ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt)))
Proof step 67:
dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), root[path] = dnode(md0, sdt), ((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs|(root, ROOT_INO, path, m) * abs(sdt, entries)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), m ∈ dirs0, path ∈ root, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced0 → asynced0 ⊦ abs(root[path, dnode(md, sdt)], ROOT_INO)(dirs)

Rule argument

Additional information

Used simplifier rules: abs-unfold: ⊦ ispath(p, ROOT_INO, ino, dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, m0, m1, entries) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ ¬ abs(tree0, ROOT_INO)(dirs0) → ( abs(tree, ROOT_INO)(dirs) ↔ (∃ sdt. (( abs|(tree, ROOT_INO, p, ino) * ino => mkdir(n, md, m0, m1, entries) * abs(sdt, entries)) )(dirs) ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt)));% ⊦ dnode(md, sdt).entries = sdt; (s)% ⊦ dnode(md, sdt).dir?; (s)%⊦ dirs ≡ dirs0[ino, ad] → ( ((ino => ad0 * D))(dirs0) ↔ ((ino => ad * D))(dirs) ∧ dirs0[ino] = ad0 ∧ ino ∈ dirs0); (ws)% ⊦ ((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]% ⊦ tree.dir? → tree.meta:= md = dnode(md, tree.entries); (s)