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Proof step 3 from proof of-cons-reduce (previous step)

of-cons(of0, dirs0, files0) ⊦ of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1)

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:
of-cons(of0, dirs0, files0) ⊦ (∀ n. n ∈ of1 → of1[n].ino ∈ files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1)

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] → [files1, dirs1, of1] flags: <all paths>

Additional information

Used terms: files1, dirs1, of1