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Proof step 158 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⌝ ), ((m9 => mkdir(# entries, root[q].meta, # links(m9, dirs), m4, entries) * abs(root[q].entries, entries) * abs|(root, ROOT_INO, 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), str ∈ root[q].entries, entries[str] ∈ files, str ' ∈ root[q], m ∈ files, ROOT_INO ∈ dirs, q ∈ root, str ∈ entries, 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 159:
root[q + str '] = fnode(⌜m⌝ ), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), files[m] = mkfile(m0, md1, # links(m, dirs), content), root[q] = dnode(md, sdt), ((m9 => mkdir(# entries, md, # links(m9, dirs), m4, entries) * abs(sdt, entries) * abs|(root, ROOT_INO, q, m9)))(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), str ∈ entries, q ∈ root, ROOT_INO ∈ dirs, m ∈ files, str ' ∈ root[q], entries[str] ∈ files, str ∈ sdt, 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: directory-tree name: dnode-elim seq: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt) subst: [tree, md, sdt] → [root[q], md0, sdt]

Additional information

Used simplifier rules: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt); (elim) Used terms: root[q], md0, sdt