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Proof step 209 from proof refine-link (previous step)

dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino2] = mkdir(# entries, md1, # links(ino2, dirs), m3, entries), root[q0].dir?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), ispath(q0, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, q0, ROOT_INO, dirs, files), ino2 ∈ dirs, str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ files, psynced → asynced, ¬ px(user, md1) ∨ ¬ pw(user, md1), links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ pre-link(q + str ', q0 + str0 ', EACCESS, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := EACCESS; if err0 = ESUCCESS then let fid = root[q + str '].fid in root[q0 + str0 '] := fnode(fid); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EACCESS = err0), root[q + str '].dir?, entries0[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 210:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (px(user, p, tree, abs-files(files)) ↔ px(user, p, ino, dirs, files))
Proof step 211:
⊦ 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 212:
dirs[ino2] = mkdir(# entries, md1, # links(ino2, dirs), m3, entries), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, ino2 ∈ dirs, ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, ¬ px(user, md1) ∨ ¬ pw(user, md1) ⊦ (¬ px(user, q, ROOT_INO, dirs, files) ∨ ¬ py(user, q0, ROOT_INO, dirs, files)) ∧ ⟨err0 := EACCESS; if err0 = ESUCCESS then let fid = root[q + str '].fid in root[q0 + str0 '] := fnode(fid); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EACCESS = err0)

Rule argument

Additional information

Used simplifier rules: px: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( px(user, p, tree, abs-files(files)) ↔ px(user, p, ino, dirs, files));%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));%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ parent(p + str ') = p; (s)%⊦ pre-link(p, p', EACCESS, user, root, fs, ofh) ↔ ¬ px(user, parent(p), root, fs) ∨ ¬ py(user, parent(p'), root, fs); (s)