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Proof step 189 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), ((abs|(root, ROOT_INO, p0, m1) * abs(root[p0], m1)))(dirs), root[p0].dir?, root.dir?, dom of < ino6, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, entries0[str], dirs, files), ispath(p0, ROOT_INO, m1, 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, p0 ∈ root, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[p0][str '] = fnode(⌜entries0[str]⌝ ), root[path].dir?, entries0[str] ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 190:
⊦ tree.dir? → abs(tree, ino) = _∃(λ ad. ino => ad * abs(tree.entries, ad.entries) ∧ ⌜ad.meta = tree.meta⌝ ∧ ⌜ad.size = # ad.entries⌝ )
Proof step 191:
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), (( abs|(root, ROOT_INO, p0, m1) * _∃(λ ad. m1 => ad * abs(root[p0].entries, ad.entries) ∧ ⌜ad.meta = root[p0].meta⌝ ∧ ⌜ad.size = # ad.entries⌝ )) )(dirs), root.dir?, root[p0].dir?, dom of < ino6, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(p0, ROOT_INO, m1, dirs, files), ispath(path, ROOT_INO, entries0[str], dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), p0 ∈ root, entries0[str] ∈ files, ROOT_INO ∈ dirs, str ∈ entries0, m1 ∈ dirs, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[p0][str '] = fnode(⌜entries0[str]⌝ ), root[path].dir?, entries0[str] ∈ dirs

Rule argument

spec: vfs-abs name: abs-is-dnode seq: ⊦ tree.dir? → abs(tree, ino) = _∃ (λ ad. ino => ad * abs(tree.entries, ad.entries) ∧ ⌜ad.meta = tree.meta⌝ ∧ ⌜ad.size = # ad.entries⌝ ) subst: [ino, tree] → [m1, root[p0]] flags: <all paths>

Additional information

Used terms: m1, root[p0]