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Proof step 1 from proof heap-order-pull-up-child (conclusion)

n ≤ # kar, m < n ⊦ heap-order(kar, n) ∧ 2 * m + 1 < n ∧ ki = (2 * m + 2 < n ∧ kar[2 * m + 2].key < kar[2 * m + 1].key ⊃ kar[2 * m + 2];kar[2 * m + 1]) → (¬ heap-order(kar[m, ki], n) ↔ false)

System applied rule normalize

And obtained the following new goals

Proof step 2:
ki = (2 * m + 2 < n ∧ kar[2 * m + 2].key < kar[2 * m + 1].key ⊃ kar[2 * m + 2];kar[2 * m + 1]), 2 * m + 1 < n, m < n, heap-order(kar, n), n ≤ # kar ⊦ ¬ heap-order(kar[m, ki], n) ↔ false

Proof step 1 from proof heap-order-pull-up-child (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information