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Proof step 18 from proof heap-order-overwrite0 (previous step)

kar[m0 + 1] = key-index(key0, m2), kar[0] = key-index(key2, m4), kar[m0 / 2] = key-index(key1, m3), m0 + 1 < # kar, m0 + 1 < n, key0 < key1, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ m0 = 0, m0 = 1, key2 < key

Heuristic quantifier applied rule all left

And closed the goal!

Rule argument

pos: left 8 terms: m0 + 1

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s)% ⊦ key-index(key, m).key = key; (s) Used terms: m0 + 1