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Proof step 13 from proof heap-order-pull-down-parent (previous step)

m2 / 2 = m1 + 1, kar[m2 + 1] = key-index(key, m0), kar[m1 / 2] = key-index(key0, m3), m1 + 1 < # kar, m2 + 1 < # kar, m2 + 1 < n, key < key0, m1 + 1 < n, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦

Heuristic quantifier applied rule all left

And obtained the following new goals

Proof step 14:
m2 / 2 = m1 + 1, kar[m1 / 2] = key-index(key0, m3), kar[m2 + 1] = key-index(key, m0), m1 + 1 < n, key < key0, m2 + 1 < n, m2 + 1 < # kar, m1 + 1 < # kar, n ≤ # kar, m2 + 1 < n ∧ m2 + 1 ≠ 0 → ¬ kar[m2 + 1].key < kar[(m2 + 1 - 1) / 2].key, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦

Rule argument

pos: left 10 terms: m2 + 1

Additional information

Used terms: m2 + 1