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Proof step 5 from proof dir-not-open (previous step)

afs-cons(dirs, files), is-open(ino, of), ino ∈ dirs, ∀ n. n ∈ of → of[n].ino ∈ files ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is-open(ino, of) ↔ (∃ n. n ∈ of ∧ of[n].ino = ino)
Proof step 7:
afs-cons(dirs, files), ino ∈ dirs, ∀ n. n ∈ of → of[n].ino ∈ files, ∃ n. n ∈ of ∧ of[n].ino = ino ⊦

Rule argument

spec: <toplevel> name: is-open seq: ⊦ is-open(ino, of) ↔ (∃ n. n ∈ of ∧ of[n].ino = ino) subst: [of, ino] → [of, ino] flags: <all paths>

Additional information

Used terms: of, ino