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Proof step 7 from proof keyset-overwrite-add (previous step)

m0 < # kar, n < # kar, m0 < # kar[n, ki], n ≤ m0, ∀ n, kar, ki. n < m0 ∧ n < # kar ∧ m0 ≤ # kar → keyset(kar[n, ki], m0) ++ kar[n] = keyset(kar, m0) ++ ki ⊦ keyset(kar[n, ki], m0) ++ kar[n, ki][m0] ++ kar[n] = keyset(kar, m0) ++ kar[m0] ++ ki

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
n < # kar, m0 < # kar, n ≤ m0, ∀ n, kar, ki. n < m0 ∧ n < # kar ∧ m0 ≤ # kar → keyset(kar[n, ki], m0) ++ kar[n] = keyset(kar, m0) ++ ki ⊦ keyset(kar[n, ki], m0) ++ kar[n, ki][m0] ++ kar[n] = keyset(kar, m0) ++ kar[m0] ++ ki

Rule argument

Additional information

Used simplifier rules: ⊦ # kar[n, ki] = # kar; (s)