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Proof step 4 from proof key-set-extract-index (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
ki ∈ keyset(kar, n0) ↔ (∃ m. m < n0 ∧ ki = kar[m]), n0 < # kar ⊦ ki = kar[n0] ∨ ki ∈ keyset(kar, n0) ↔ (∃ m. ¬ n0 < m ∧ ki = kar[m])

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)