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Proof step 97 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 ⊦ dom entries = dom sdt

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 98:
⊦ strings = strings0 ↔ (∀ str. str ∈ strings ↔ str ∈ strings0)
Proof step 99:
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

Rule argument

spec: set-basic, inst: dir-entries name: Extension seq: ⊦ strings = strings0 ↔ (∀ str. str ∈ strings ↔ str ∈ strings0) subst: [strings0, strings] → [dom sdt, dom entries] flags: <all paths>

Additional information

Used terms: dom sdt, dom entries