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Proof step 10 from proof union-subset (previous step)

union(asar, n, m0) ⊆ as ↔ (∀ n0. n ≤ n0 ∧ n0 < n + m0 → asar[n0] ⊆ as), ∀ n0. n ≤ n0 ∧ ¬ n + m0 < n0 → asar[n0] ⊆ as ⊦ asar[n + m0] ⊆ as ∧ union(asar, n, m0) ⊆ as

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information