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Proof step 12 from proof in-keys (previous step)

m < # zbrar, m + nused0 < # zbrar ⊦ zbrar[m].key ∈ keys(zbrar, m + 1, nused0), ∃ n. ¬ nused0 < n ∧ zbrar[m + n].key = zbrar[m].key, ∃ n. n < nused0 ∧ zbrar[(m + 1) + n].key = zbrar[m].key

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: 0

Additional information

Used simplifier rules: ⊦ ¬ m < 0; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: 0