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Proof step 163 from proof refine-readmeta (previous step)

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), sdt[str] = fnode(⌜entries[str]⌝ ), ((m9 => mkdir(# entries, md, # links(m9, dirs), m4, entries) * abs(sdt -- str, entries -- str) * abs|(root, ROOT_INO, q, m9)))(dirs), root.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 ∈ sdt, entries[str] ∈ files, str ∈ entries, q ∈ root, ROOT_INO ∈ dirs, m ∈ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: directory-tree name: split-at seq: ⊦ p ∈ tree → tree[p + q] = tree[p][q] subst: [q, p, tree] → [str ', q, root] flags: <all paths>

Additional information

Used simplifier rules: str ∈ sdt ⊦ dnode(md, sdt)[str '] = sdt[str]; (s)% ⊦ fnode(fid) = fnode(fid0) ↔ fid = fid0; (s)% ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s) Used terms: str ', q, root