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Proof step 61 from proof prepost-resize (previous step)

kar[1 + m1] = key-index(key, m0), copy(kar, 0, mkkeyarray(n0), 0, m)[m1 / 2] = key-index(key0, m2), 2exp-size(n0), 2exp-size(# kar), 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 ⊦ m1 / 2 < # mkkeyarray(n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
kar[1 + m1] = key-index(key, m0), kar[m1 / 2] = key-index(key0, m2), 2exp-size(# kar), 2exp-size(n0), m1 + 1 < # kar, m1 + 1 < minsize, m < n0, m < minsize, m1 + 1 < m, key < key0, 2 + m1 < n0, 2 + m1 < minsize, m1 + 1 < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0, n0 * 2 ≤ m1 ⊦

Rule argument

Additional information

Used simplifier rules: m0 ≠ 0 ⊦ n ≤ m / m0 ↔ n * m0 ≤ m; (s)%# kar = m, # kar0 = m ⊦ copy(kar, 0, kar0, 0, m) = kar; (s)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + 1 < m / 2; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # mkkeyarray(n) = n; (s)