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Proof step 8 from proof key-set-extract-index (previous step)

kar[n0] ∈ keyset(kar, n0) ↔ (∃ m. m < n0 ∧ kar[n0] = kar[m]), n0 < # kar ⊦ ∃ m. ¬ n0 < m ∧ kar[n0] = kar[m]

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: n0

Additional information

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