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Proof step 10 from proof valid-indices-nonrec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information