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Proof step 4 from proof key-set-in (previous step)

bh = bin-heap(kar, m0), 2exp-size(# kar), heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), m0 ≤ # kar ⊦ ki ∈ keyset(kar, m0) ↔ (∃ m. m < m0 ∧ ki = kar[m])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
2exp-size(# kar), heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), m0 ≤ # kar ⊦ ki ∈ keyset(kar, m0) ↔ (∃ m. m < m0 ∧ ki = kar[m])

Proof step 4 from proof key-set-in (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information