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Proof step 176 from proof refine-readmeta (previous step)

dirs[m1] = mkdir(# entries0, md0, # links(m1, dirs), m7, entries0), 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), root[p0].dir?, 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, 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), m1 ∈ dirs, str ∈ entries0, ROOT_INO ∈ dirs, entries0[str] ∈ files, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[path].dir?, entries0[str] ∈ dirs, p0 + str ' ∈ links(⌜entries0[str]⌝ , root)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 177:
⊦ p ∈ links(fid, tree) ↔ p ∈ tree ∧ tree[p] = fnode(fid)
Proof step 178:
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), dirs[m1] = mkdir(# entries0, md0, # links(m1, dirs), m7, entries0), root.dir?, root[p0].dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), 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), entries0[str] ∈ files, ROOT_INO ∈ dirs, str ∈ entries0, m1 ∈ dirs, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[path].dir?, entries0[str] ∈ dirs, p0 + str ' ∈ root ∧ root[p0 + str '] = fnode(⌜entries0[str]⌝ )

Rule argument

spec: posix-links name: in-plinks seq: ⊦ p ∈ links(fid, tree) ↔ p ∈ tree ∧ tree[p] = fnode(fid) subst: [tree, fid, p] → [root, ⌜entries0[str]⌝ , p0 + str '] flags: <all paths>

Additional information

Used terms: root, ⌜entries0[str]⌝ , p0 + str '