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Proof step 16 from proof inv-format (previous step)

⊦ of-cons(∅, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ of-cons(of, dirs, files) ↔ (∀ n. n ∈ of → of[n].ino ∈ files)

Rule argument

spec: vfs-base name: of-cons seq: ⊦ of-cons(of, dirs, files) ↔ (∀ n. n ∈ of → of[n].ino ∈ files) subst: [files, dirs, of] → [∅, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ fd ∈ ∅; (s) Used terms: ∅, (∅ ++ ROOT_INO)[ROOT_INO, mkdir(0, md, 0, 0, ∅)], ∅