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Proof step 175 from proof refine-create (previous step)

dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m3, entries0), fs = abs-files(files0), path = q + str ', ino2 ≠ 0, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino1 ∈ dirs0, dirs ≡ dirs0[ino1, mkdir(# entries0 + 1, md0, # links(ino1, dirs0), m3, entries0[str, ino2])], ¬ ino2 ∈ files0, ¬ str ∈ entries0, ¬ ino2 ∈ dirs, ¬ ino2 ∈ dirs0, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ∃ err. pre-create(path, md, err, user, root, fs, abs-of(of)) ∧ ⟨err0 := err; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files((files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), ¬ ispath(path, ROOT_INO, dirs0, files0) ∧ ispath(parent(path), ROOT_INO, dirs0, files0) ∧ root[parent(path)].dir? ∧ py(user, parent(path), root, fs) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files((files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 176:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (py(user, p, tree, abs-files(files)) ↔ py(user, p, ino, dirs, files))
Proof step 177:
⊦ ispath(q, ino, m, dirs, files) ∧ px-parent(user, q, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (py(user, q, ino, dirs, files) ↔ pw(user, meta(ε, m, dirs, files)) ∧ px(user, meta(ε, m, dirs, files)))
Proof step 178:
dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m3, entries0), fs = abs-files(files0), path = q + str ', root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs, (files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino1 ∈ dirs0, dirs ≡ dirs0[ino1, mkdir(# entries0 + 1, md0, # links(ino1, dirs0), m3, entries0[str, ino2])], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files((files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), ∃ err. pre-create(path, md, err, user, root, fs, abs-of(of)) ∧ ⟨err0 := err; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files((files0 ++ ino2)[ino2, mkfile(0, md, 1, ∅)]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), ino2 = 0, ino2 ∈ files0, str ∈ entries0, ino2 ∈ dirs, ino2 ∈ dirs0

Rule argument

pos: right 2

Additional information

Used simplifier rules: py: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( py(user, p, tree, abs-files(files)) ↔ py(user, p, ino, dirs, files));%py-strong: ⊦ ispath(q, ino, m, dirs, files) ∧ px-parent(user, q, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( py(user, q, ino, dirs, files) ↔ pw(user, meta(ε, m, dirs, files)) ∧ px(user, meta(ε, m, dirs, files)));% ⊦ parent(p + str ') = p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ ino ∈ dirs → meta(ε, ino, dirs, files) = dirs[ino].meta; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)%⊦ ispath(p, n, m, dirs, files) → (ispath(p + q, n, dirs, files) ↔ ispath(q, m, dirs, files)); (s)%⊦ ispath(str ', n, dirs, files) ↔ n ∈ dirs ∧ str ∈ dirs[n].entries ∧ (dirs[n].entries[str] ∈ dirs ∨ dirs[n].entries[str] ∈ files); (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)