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Proof step 3 from proof dir-not-open (previous step)

afs-cons(dirs, files), is-open(ino, of), of-cons(of, dirs, files), ino ∈ dirs ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ of-cons(of, dirs, files) ↔ (∀ n. n ∈ of → of[n].ino ∈ files)
Proof step 5:
afs-cons(dirs, files), is-open(ino, of), ino ∈ dirs, ∀ n. n ∈ of → of[n].ino ∈ files ⊦

Rule argument

spec: <toplevel> name: of-cons seq: ⊦ of-cons(of, dirs, files) ↔ (∀ n. n ∈ of → of[n].ino ∈ files) subst: [files, dirs, of] → [files, dirs, of] flags: <all paths>

Additional information

Used terms: files, dirs, of