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Proof step 7 from proof heap-order-min (previous step)

kar[0] = key-index(key0, m2), kar[m] = key-index(key, m1), n0 < # kar, key < key0, m < # kar, m ≤ n0, kar[(m - 1) / 2].key < kar[0].key ∧ (m - 1) / 2 < n0 ∧ (∀ m. m < n0 ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key) ∧ n0 ≤ # kar → (m - 1) / 2 = 0, ∀ m0. ¬ n0 < m0 ∧ m0 ≠ 0 → ¬ kar[m0].key < kar[(m0 - 1) / 2].key ⊦ m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
kar[0] = key-index(key0, m2), kar[m] = key-index(key, m1), n0 < # kar, key < key0, m < # kar, m ≤ n0, kar[(m - 1) / 2].key < key0 ∧ (m - 1) / 2 < n0 ∧ (m0 < n0 ∧ m0 ≠ 0 → ¬ kar[m0].key < kar[(m0 - 1) / 2].key) → m - 1 = 0 ∨ m - 1 = 1, ∀ m0. ¬ n0 < m0 ∧ m0 ≠ 0 → ¬ kar[m0].key < kar[(m0 - 1) / 2].key ⊦ m = 0

Rule argument

Additional information

Used simplifier rules: ⊦ key-index(key, m).key = key; (s)% ⊦ m / 2 = 0 ↔ m = 0 ∨ m = 1; (s)% ⊦ m < n → m ≤ n; (s)