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Proof step 7 from proof key-set-write-other (previous step)

m0 + 1 < # kar, n < # kar, m0 < n, m0 < # kar, m0 < # kar[n, ki], ∀ kar, n, ki. m0 < # kar ∧ n < # kar ∧ m0 ≤ n → keyset(kar[n, ki], m0) = keyset(kar, m0) ⊦ keyset(kar[n, ki], m0) ++ kar[n, ki][m0] = keyset(kar, m0) ++ kar[m0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
m0 < n, n < # kar, m0 + 1 < # kar, m0 < # kar, ∀ kar, n, ki. m0 < # kar ∧ n < # kar ∧ m0 ≤ n → keyset(kar[n, ki], m0) = keyset(kar, m0) ⊦ keyset(kar[n, ki], m0) ++ kar[m0] = keyset(kar, m0) ++ kar[m0]

Rule argument

Additional information

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