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Proof step 5 from proof valid-indices-append (previous step)

⊦ (∀ n. n ∈ nx0 + nx1 → n < # ar) ↔ nx0 < # ar ∧ nx1 < # ar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ (∀ n. n ∈ nx0 ∨ n ∈ nx1 → n < # ar) ↔ nx0 < # ar ∧ nx1 < # ar

Rule argument

Additional information

Used simplifier rules: a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ n ∈ nx + nx0 ↔ n ∈ nx ∨ n ∈ nx0; (s)