[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 470 from proof refine-unlink (previous step)

⟨files := files -- ino⟩ (ESUCCESS = err2 ∧ dirs = dirs1 ∧ files = files1), # entries0 = m0 + 1, # links(entries0[str], dirs0) = m + 1, files[ino].nlink = 0, files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), dirs = dirs1, err = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], ino = inode.ino, inode = getinode(entries0[str], dirs1, files), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs1, files1), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs1, files1), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries0, ino1 ∈ dirs0, entries0[str] ∈ files0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], psynced → asynced0 ⊦ # links(ino1, dirs0) = 0, entries0 = ∅, ino1 = ROOT_INO, links(ino1, dirs0) = ∅, root[q + str '].dir?, is-open(entries0[str], of), pre-unlink(q + str ', err2, user, root, abs-files(files0), abs-of(of)), ino ∈ dirs, entries0[str] ∈ dirs0, ino1 ∈ dirs1, entries0[str] ∈ dirs1

Heuristic symbolic execution applied rule assign left

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: path-in-last: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries);%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)));%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)%ino ∈ files ⊦ files[ino, af] -- ino = files -- ino; (s)%⊦ pre-unlink(p, ESUCCESS, user, root, fs, ofh) ↔ p ≠ ε ∧ p ∈ root ∧ ¬ root[p].dir? ∧ py(user, parent(p), root, fs); (s)% ⊦ p + str ' ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ parent(p + str ') = p; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ ino ∈ dirs → meta(ε, ino, dirs, files) = dirs[ino].meta; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)