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Proof step 2 from proof heap-order-overwrite0 (previous step)

heap-order(kar, n), n ≤ # kar ⊦ n = 0, kar[0].key < ki.key, heap-order(kar[0, ki], n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
kar[m].key < kar[0, ki][(m - 1) / 2].key, m < n, m < # kar, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ m = 0, kar[0].key < ki.key

Rule argument

Additional information

Used simplifier rules: heap-order: ⊦ heap-order(kar, n) ↔ (∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key);%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m ≠ n → kar[n, ki][m] = kar[m]; (s)