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Proof step 17 from proof valid-indices-append (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# ar ≤ n, ∀ n. n ∈ nx1 → n < # ar, ∀ n. n ∈ nx0 → n < # ar, n ∈ nx0 ∨ n ∈ nx1 ⊦

Rule argument

Additional information

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