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Proof step 8 from proof of-cons-reduce (previous step)

∀ n. n ∈ of0 → of0[n].ino ∈ files0 ⊦ (∀ n. n ∈ of1 → of1[n].ino ∈ files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1)

User applied rule case distinction

And obtained the following new goals

Proof step 9:
∀ n. n ∈ of0 → of0[n].ino ∈ files0, ∀ n. n ∈ of1 → of1[n].ino ∈ files1 ⊦ ∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1
Proof step 13:
∀ n. n ∈ of0 → of0[n].ino ∈ files0, ∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1 ⊦ ∀ n. n ∈ of1 → of1[n].ino ∈ files1

Rule argument

pos: right 1

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