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Proof step 4 from proof heap-order-overwrite0 (previous step)

m = m0 + 1, m < # kar, m < n, kar[m].key < kar[0, ki][m0 / 2].key, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ m = 0, kar[0].key < ki.key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
kar[m0 + 1].key < kar[0, ki][m0 / 2].key, m0 + 1 < n, m0 + 1 < # kar, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ kar[0].key < ki.key

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)