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Proof step 2 from proof keyset-xchg (previous step)

kar[n0] = ki1, kar[n1] = ki0, n0 < m, n1 < m, m ≤ # kar ⊦ keyset(kar[n0, ki0][n1, ki1], m) = keyset(kar, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n1 < m, n0 < m, n1 < # kar, n0 < # kar, m ≤ # kar ⊦ keyset(kar[n0, kar[n1]][n1, kar[n0]], m) = keyset(kar, m)

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