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Proof step 192 from proof refine-readmeta (previous step)

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), ((m1 => mkdir(# entries0, root[p0].meta, # links(m1, dirs), m7, entries0) * abs(root[p0].entries, entries0) * abs|(root, ROOT_INO, 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), str ∈ root[p0].entries, ROOT_INO ∈ dirs, entries0[str] ∈ files, p0 ∈ root, str ∈ entries0, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[p0][str '] = fnode(⌜entries0[str]⌝ ), root[path].dir?, entries0[str] ∈ dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 193:
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), root[p0] = dnode(md0, sdt), ((m1 => mkdir(# entries0, md0, # links(m1, dirs), m7, entries0) * abs(sdt, entries0) * abs|(root, ROOT_INO, p0, m1)))(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), str ∈ entries0, p0 ∈ root, entries0[str] ∈ files, ROOT_INO ∈ dirs, str ∈ sdt, 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: directory-tree name: dnode-elim seq: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt) subst: [tree, md, sdt] → [root[p0], md1, sdt]

Additional information

Used simplifier rules: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt); (elim) Used terms: root[p0], md1, sdt