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Proof step 23 from proof keyset-subarray-eq (previous step)

keyset(kar0, m0) = keyset(kar1, m0), m0 < # kar0, m0 < # kar1, ¬ m0 < m0 → subarray(kar0, 0, m0 + 1)[m0] = subarray(kar1, 0, m0 + 1)[m0] ⊦ keyset(kar1, m0) ++ kar0[m0] = keyset(kar1, m0) ++ kar1[m0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
subarray(kar0, 0, m0 + 1)[m0] = subarray(kar1, 0, m0 + 1)[m0], keyset(kar0, m0) = keyset(kar1, m0), m0 < # kar1, m0 < # kar0 ⊦ keyset(kar1, m0) ++ kar0[m0] = keyset(kar1, m0) ++ kar1[m0]

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)