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Proof step 13 from proof valid-indices-nonrec (previous step)

∀ n. n = m ∨ n ∈ nx0 → n < # ar, ∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar) ⊦ m < # ar ∧ nx0 < # ar

User applied rule case distinction

And obtained the following new goals

Proof step 14:
∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar), ∀ n. n = m ∨ n ∈ nx0 → n < # ar ⊦ m < # ar
Proof step 16:
∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar), ∀ n. n = m ∨ n ∈ nx0 → n < # ar ⊦ nx0 < # ar

Rule argument

pos: right 1

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