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Proof step 2 from proof in-below (previous step)

⊦ n ∈ below(ns, m) ↔ n ∈ ns ∧ n < m

User applied rule induction

And obtained the following new goals

Proof step 3:
∀ ns0, n, m. # ns0 < # ns → true → (n ∈ below(ns0, m) ↔ n ∈ ns0 ∧ n < m) ⊦ n ∈ below(ns, m) ↔ n ∈ ns ∧ n < m

Rule argument

indvar: # ns wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # ns