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Proof step 2 from proof keyset-overwrite-add (previous step)

n < m, m ≤ # kar ⊦ keyset(kar[n, ki], m) ++ kar[n] = keyset(kar, m) ++ ki

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < m, n < # kar, m ≤ # kar ⊦ keyset(kar[n, ki], m) ++ kar[n] = keyset(kar, m) ++ ki

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic