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Proof step 22 from proof heap-order-overwrite-children-at (previous step)

kar[m1 + 1] = key-index(key5, m7), kar[2 * m + 1] = key-index(key3, m5), kar[m1 / 2] = key-index(key6, m8), kar[m, key-index(key, m0)][m1 + 1] = key-index(key0, m2), kar[2 * m + 2] = key-index(key2, m4), kar[(m - 1) / 2] = key-index(key4, m6), m1 + 1 < # kar, m < # kar, m1 + 1 < n, key0 < key6, m < n, n ≤ # kar, m ≠ 0 → ¬ key < key4, 2 * m + 1 < n → ¬ key3 < key, 2 * m + 2 < n → ¬ key2 < key ⊦ m1 / 2 = m, key5 < key6

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: m1 + 1 = m

Additional information

Used simplifier rules: ⊦ m ≠ n → kar[n, ki][m] = kar[m]; (s)% ⊦ key-index(key, m) = key-index(key0, m0) ↔ key = key0 ∧ m = m0; (ws)% ⊦ m * (n + 1) = m * n + m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m < # kar → kar[m, ki][m] = ki; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s)% ⊦ m / 2 ≠ m + 1; (s)% ⊦ m + 1 ≠ 0; (s)%lel: ⊦ key < key0 ∧ key = key1 → key1 < key0; (forward) from specification oelem[binheap-key] Used formulas: m1 + 1 = m