[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 210 from proof refine-readmeta (previous step)

root[p0] = fnode(⌜m⌝ ), root[q] = fnode(⌜m⌝ ), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), lookup(q0, ROOT_INO, dirs, files) = lookup(parent(q), ROOT_INO, dirs, files), p0 = q0 + str ', str = q.last, root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(p0, ROOT_INO, m9, dirs, files), ispath(q, ROOT_INO, m8, dirs, files), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m ∈ files, ROOT_INO ∈ dirs, psynced → asynced ⊦ # links(⌜m⌝ , root) = 0, # links(m, dirs) = count(⌜m⌝ , root.fids), links(⌜m⌝ , root) = ∅, p0 = q, p0 = ε, root[path].dir?, m9 ∈ dirs, m8 ∈ dirs, m ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 211:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs)
Proof step 212:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 213:
⊦ ispath(p, ino, dirs, files) ↔ (∃ m. ispath(p, ino, m, dirs, files))
Proof step 214:
root[q0 + q.last '] = fnode(⌜m⌝ ), root[q] = fnode(⌜m⌝ ), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), root[q0].dir?, root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0 + q.last ', ROOT_INO, m9, dirs, files), ispath(q, ROOT_INO, m8, dirs, files), ispath(path, ROOT_INO, m, dirs, files), ispath(q0, ROOT_INO, lookup(parent(q), ROOT_INO, dirs, files), dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), lookup(parent(q), ROOT_INO, dirs, files) ∈ dirs, q.last ' ∈ root[q0], m ∈ files, ROOT_INO ∈ dirs, psynced → asynced ⊦ # links(⌜m⌝ , root) = 0, # links(m, dirs) = count(⌜m⌝ , root.fids), q0 + q.last ' = q, links(⌜m⌝ , root) = ∅, root[path].dir?, m9 ∈ dirs, m8 ∈ dirs, m ∈ dirs

Rule argument

Additional information

Used simplifier rules: path-in: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs);%path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));%ispath-target: ⊦ ispath(p, ino, dirs, files) ↔ (∃ m. ispath(p, ino, m, dirs, files));% ⊦ ¬ fnode(fid).dir?; (s)% ⊦ str ' ≠ ε; (s)% ⊦ ¬ tree.dir? → (p ∈ tree ↔ p = ε); (s)% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)% ⊦ ispath(p, n, m, dirs, files) → lookup(p, n, dirs, files) = m; (s)% ⊦ p + q ∈ tree ↔ p ∈ tree ∧ q ∈ tree[p]; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + str ' ≠ ε; (s)