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Proof step 194 from proof refine-readmeta (previous step)

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?, 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 ∈ sdt, str ∈ entries0, p0 ∈ root, entries0[str] ∈ files, ROOT_INO ∈ dirs, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), sdt[str] = fnode(⌜entries0[str]⌝ ), root[path].dir?, entries0[str] ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: vfs-abs name: entries-recdel seq: ⊦ str ∈ sdt → abs(sdt, sdi) = ( ⌜str ∈ sdi⌝ ∧ abs(sdt -- str, sdi -- str) * abs(sdt[str], sdi[str])) subst: [str, sdi, sdt] → [str, entries0, sdt] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ⌜true⌝ = true; (s)% ⊦ (true ∧ D) = D; (s)%and-ass: ⊦ ((D ∧ D0) ∧ D1) = (D ∧ D0 ∧ D1); from specification heap-sep[dir-heap]%and-com: ⊦ (D ∧ D0) = (D0 ∧ D); from specification heap-sep[dir-heap]%⊦ ¬ ino ∈ dirs → (((abs(tree, ino) * D))(dirs) ↔ tree = fnode(⌜ino⌝ ) ∧ D(dirs)); (ws)%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap] Used terms: str, entries0, sdt