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Proof step 99 from proof refine-readdir (previous step)

root[path] = dnode(md, sdt), ((ino1 => mkdir(# entries, md, # links(ino1, dirs), m1, entries) * abs(sdt, entries) * abs|(root, ROOT_INO, path, ino1)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), path ∈ root, psynced → asynced ⊦ ∀ str. str ∈ dom entries ↔ str ∈ dom sdt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 100:
root[path] = dnode(md, sdt), ((ino1 => mkdir(# entries, md, # links(ino1, dirs), m1, entries) * abs(sdt, entries) * abs|(root, ROOT_INO, path, ino1)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), path ∈ root, psynced → asynced ⊦ str ∈ entries ↔ str ∈ sdt

Rule argument

Additional information

Used simplifier rules: ⊦ str ∈ dom sdt ↔ str ∈ sdt; (s)% ⊦ str ∈ dom entries ↔ str ∈ entries; (s)