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Proof step 14 from proof valid-indices-nonrec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# ar ≤ m, ∀ n. n = m ∨ n ∈ nx0 → n < # ar, ∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)