[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 169 from proof refine-readmeta (previous step)

dirs[m1] = mkdir(# entries0, md0, # links(m1, dirs), m7, entries0), files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, entries0[str], dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m1 ∈ dirs, str ∈ entries0, ROOT_INO ∈ dirs, entries0[str] ∈ files, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[path].dir?, entries0[str] ∈ dirs, ∃ p0. p0 ∈ links(⌜dirs[lookup(parent(p0), ROOT_INO, dirs, files)].entries[p0.last]⌝ , root) ∧ mklink(lookup(parent(p0), ROOT_INO, dirs, files), p0.last) = mklink(m1, str)

User applied rule apply lemma

And obtained the following new goals

Proof step 170:
⊦ abs(tree, ino0)(dirs) ∧ ino1 ∈ dirs → (∃ p. ispath(p, ino0, ino1, dirs, files))
Proof step 171:
dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content), dirs[m1] = mkdir(# entries0, md0, # links(m1, dirs), m7, entries0), root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, entries0[str], dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), entries0[str] ∈ files, ROOT_INO ∈ dirs, str ∈ entries0, m1 ∈ dirs, psynced → asynced, abs(root, ROOT_INO)(dirs) ∧ m1 ∈ dirs → (∃ p. ispath(p, ROOT_INO, m1, dirs, files)) ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[path].dir?, entries0[str] ∈ dirs, ∃ p0. p0 ∈ links(⌜dirs[lookup(parent(p0), ROOT_INO, dirs, files)].entries[p0.last]⌝ , root) ∧ mklink(lookup(parent(p0), ROOT_INO, dirs, files), p0.last) = mklink(m1, str)

Rule argument

spec: vfs-abs name: abs-has-rootpath seq: ⊦ abs(tree, ino0)(dirs) ∧ ino1 ∈ dirs → (∃ p. ispath(p, ino0, ino1, dirs, files)) subst: [tree, ino0, dirs, ino1, files] → [root, ROOT_INO, dirs, m1, files]

Additional information

Used terms: root, ROOT_INO, dirs, m1, files