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Proof step 8 from proof valid-indices-nonrec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information