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Proof step 197 from proof refine-readmeta (previous step)

p0.last = q.last, dirs[m1] = mkdir(m5, md0, m6, m7, entries0), files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), lookup(parent(p0), ROOT_INO, dirs, files) = lookup(parent(q), ROOT_INO, dirs, files), root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), p0 ∈ links(⌜m⌝ , root), q ∈ links(⌜m⌝ , root), ROOT_INO ∈ dirs, m ∈ files, psynced → asynced ⊦ # links(m, dirs) = count(⌜m⌝ , root.fids), # links(⌜m⌝ , root) = 0, links(⌜m⌝ , root) = ∅, p0 = q, root[path].dir?, m ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 198:
⊦ p ∈ links(fid, tree) ↔ p ∈ tree ∧ tree[p] = fnode(fid)
Proof step 199:
p0.last = q.last, root[q] = fnode(⌜m⌝ ), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), lookup(parent(p0), ROOT_INO, dirs, files) = lookup(parent(q), ROOT_INO, dirs, files), root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m ∈ files, ROOT_INO ∈ dirs, q ∈ root, p0 ∈ links(⌜m⌝ , root), psynced → asynced ⊦ # links(⌜m⌝ , root) = 0, # links(m, dirs) = count(⌜m⌝ , root.fids), links(⌜m⌝ , root) = ∅, p0 = q, root[path].dir?, m ∈ dirs

Rule argument

spec: posix-links name: in-plinks seq: ⊦ p ∈ links(fid, tree) ↔ p ∈ tree ∧ tree[p] = fnode(fid) subst: [tree, fid, p] → [root, ⌜m⌝ , q] flags: <all paths>

Additional information

Used terms: root, ⌜m⌝ , q