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Proof step 18 from proof lookup-range-rem-union (previous step)

key ∈ ri ⊦ key ∈ ks, ∃ key0. key0 ∈ ri \ ks ∧ (ri \ ks)[key0] = ri[key]

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: key

Additional information

Used simplifier rules: ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ws)% ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key]; (s) Used terms: key