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Proof step 76 from proof refine-writemeta (previous step)

root[path] = dnode(md0, sdt), dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), ((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs|(root, ROOT_INO, path, m) * abs(sdt, entries)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), path ∈ root, m ∈ dirs0, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced0 → asynced0 ⊦ (((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs(sdt, entries)) * abs|(root[path, dnode(md, sdt)], ROOT_INO, path, m)) )(dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
⊦ p ≠ ε ∧ q ⊑ p ∧ parent(p) ∈ tree ∧ tree[parent(p)].dir? → abs|(tree[p, tree0], ino0, q, ino1) = abs|(tree, ino0, q, ino1)
Proof step 78:
dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), root[path] = dnode(md0, sdt), ((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs|(root, ROOT_INO, path, m) * abs(sdt, entries)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), m ∈ dirs0, path ∈ root, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced0 → asynced0 ⊦ (((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs(sdt, entries)) * abs|(root[path, dnode(md, sdt)], ROOT_INO, path, m)) )(dirs), path ≠ ε ∧ path ⊑ path ∧ parent(path) ∈ root ∧ root[parent(path)].dir?

Rule argument

spec: vfs-abs name: absc-drop seq: ⊦ p ≠ ε ∧ q ⊑ p ∧ parent(p) ∈ tree ∧ tree[parent(p)].dir? → abs|(tree[p, tree0], ino0, q, ino1) = abs|(tree, ino0, q, ino1) subst: [ino1, q, ino0, tree0, p, tree] → [m, path, ROOT_INO, dnode(md, sdt), path, root] flags: <all paths>

Additional information

Used simplifier rules: 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: m, path, ROOT_INO, dnode(md, sdt), path, root