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Proof step 8 from proof in-union-ext (previous step)

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

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 6 terms: n + m0

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s) Used terms: n + m0