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Proof step 68 from proof prepost-resize (previous step)

kar[1 + m1] = key-index(key, m0), kar[m1 / 2] = key-index(key0, m2), 2exp-size(n0), 2exp-size(# kar), m1 / 2 < n0, m1 + 1 < n0, 2 + m1 < minsize, 2 + m1 < n0, key < key0, m1 + 1 < m, m < minsize, m < n0, m1 + 1 < minsize, m1 + 1 < # kar, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦ m * 2 ≤ m1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 69:
kar[1 + m1] = key-index(key, m0), kar[m1 / 2] = key-index(key0, m2), 2exp-size(n0), 2exp-size(# kar), m1 < m * 2, m1 / 2 < n0, m1 + 1 < n0, 2 + m1 < minsize, 2 + m1 < n0, key < key0, m1 + 1 < m, m < minsize, m < n0, m1 + 1 < minsize, m1 + 1 < # kar, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m < n → n ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)