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Proof step 6 from proof heap-order-add-smaller (previous step)

n = m1 + 1, m0 + 1 < # kar, n < # kar, m0 < n, kar[n, ki][m0 + 1].key < kar[m0 / 2].key, m0 < # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ n = 0, ki.key < kar[m1 / 2].key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m1 + 1 < # kar, m0 + 1 < # kar, m0 < # kar, kar[m1 + 1, ki][m0 + 1].key < kar[m0 / 2].key, m0 ≤ m1, ∀ m. ¬ m1 < m ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ ki.key < kar[m1 / 2].key

Rule argument

Additional information

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