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Proof step 18 from proof valid-indices-append (previous step)

# ar ≤ n, ∀ n. n ∈ nx1 → n < # ar, ∀ n. n ∈ nx0 → n < # ar, n ∈ nx0 ∨ n ∈ nx1 ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 19:
n ∈ nx0, # ar ≤ n, ∀ n. n ∈ nx0 → n < # ar, ∀ n. n ∈ nx1 → n < # ar ⊦
Proof step 20:
n ∈ nx1, # ar ≤ n, ∀ n. n ∈ nx0 → n < # ar, ∀ n. n ∈ nx1 → n < # ar ⊦

Rule argument

pos: left 4

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