[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 62 from proof refine-readmeta (previous step)

root[path] = dnode(md, sdt), dirs[m] = mkdir(# entries, md1, # links(m, dirs), m2, entries), ((abs|(root, ROOT_INO, path, m) * abs(dnode(md, sdt), m)))(dirs), root.dir?, dom of < ino6, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m ∈ dirs, path ∈ root, psynced → asynced ⊦ md1 = md ∧ m2 = # dnode(md, sdt).subdirs ∧ # entries = # sdt

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ abs(dnode(md, sdt), ino) = _∃(λ ad. ino => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ )
Proof step 64:
dirs[m] = mkdir(# entries, md1, # links(m, dirs), m2, entries), root[path] = dnode(md, sdt), ((abs|(root, ROOT_INO, path, m) * _∃(λ ad. m => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ )))(dirs), root.dir?, dom of < ino6, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), path ∈ root, m ∈ dirs, psynced → asynced ⊦ md1 = md ∧ m2 = # dnode(md, sdt).subdirs ∧ # entries = # sdt

Rule argument

spec: vfs-abs name: abs-dnode seq: ⊦ abs(dnode(md, sdt), ino) = _∃ (λ ad. ino => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ ) subst: [ino, sdt, md] → [m, sdt, md] flags: <all paths>

Additional information

Used terms: m, sdt, md