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Proof step 71 from proof refine-writemeta (previous step)

root[path] = dnode(md0, sdt), dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), ((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs|(root, ROOT_INO, path, m) * abs(sdt, entries)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), path ∈ root, m ∈ dirs0, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced0 → asynced0 ⊦ ((abs|(root[path, dnode(md, sdt)], ROOT_INO, path, m) * abs(dnode(md, sdt), m)))(dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

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