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Proof step 155 from proof refine-readmeta (previous step)

files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), root[q + str '] = fnode(⌜m⌝ ), dirs[m9] = mkdir(# entries, md, # links(m9, dirs), m4, entries), ((abs|(root, ROOT_INO, q, m9) * abs(root[q], m9)))(dirs), root[q].dir?, root.dir?, dom of < ino6, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, m9, dirs, files), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), entries[str] ∈ files, str ∈ entries, m9 ∈ dirs, str ' ∈ root[q], m ∈ files, ROOT_INO ∈ dirs, q ∈ root, psynced → asynced ⊦ # links(⌜m⌝ , root) = 0, # links(m, dirs) = count(⌜m⌝ , root.fids), links(⌜m⌝ , root) = ∅, m = entries[str], root[path].dir?, entries[str] ∈ dirs, m ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 156:
⊦ tree.dir? → abs(tree, ino) = _∃(λ ad. ino => ad * abs(tree.entries, ad.entries) ∧ ⌜ad.meta = tree.meta⌝ ∧ ⌜ad.size = # ad.entries⌝ )
Proof step 157:
dirs[m9] = mkdir(# entries, md, # links(m9, dirs), m4, entries), root[q + str '] = fnode(⌜m⌝ ), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), files[m] = mkfile(m0, md1, # links(m, dirs), content), ((abs|(root, ROOT_INO, q, m9) * _∃(λ ad. m9 => ad * abs(root[q].entries, ad.entries) ∧ ⌜ad.meta = root[q].meta⌝ ∧ ⌜ad.size = # ad.entries⌝ )) )(dirs), root.dir?, root[q].dir?, dom of < ino6, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), ispath(q, ROOT_INO, m9, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), q ∈ root, ROOT_INO ∈ dirs, m ∈ files, str ' ∈ root[q], m9 ∈ dirs, str ∈ entries, entries[str] ∈ files, psynced → asynced ⊦ # links(m, dirs) = count(⌜m⌝ , root.fids), # links(⌜m⌝ , root) = 0, links(⌜m⌝ , root) = ∅, m = entries[str], root[path].dir?, m ∈ dirs, entries[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] → [m9, root[q]] flags: <all paths>

Additional information

Used terms: m9, root[q]