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Proof step 10 from proof in-union-ext (previous step)

n0 < n + m0, adr ∈ asar[n + m0] ∪ union(asar, n, m0), adr ∈ union(asar, n, m0), adr ∈ asar[n0], n ≤ n0 ⊦ #(asar[n + m0] ∪ union(asar, n, m0)) = 0, # union(asar, n, m0) = 0, # asar[n0] = 0, asar[n0] = ∅, m0 = 0, union(asar, n, m0) = ∅, asar[n + m0] ∪ union(asar, n, m0) = ∅, ∃ n0. n ≤ n0 ∧ ¬ n + m0 < n0 ∧ adr ∈ asar[n0]

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 8 terms: n0

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s) Used terms: n0