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Proof step 64 from proof prepost-resize (previous step)

(m1 / 2 < 0 ∨ 0 + m ≤ m1 / 2 ⊃ mkkeyarray(n0)[m1 / 2];kar[m1 / 2 + 0 - 0]) = key-index(key0, m2), kar[1 + m1] = key-index(key, m0), 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, m1 / 2 < # mkkeyarray(n0), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
(m * 2 ≤ m1 ⊃ mkkeyarray(n0)[m1 / 2];kar[m1 / 2]) = key-index(key0, m2), kar[1 + m1] = key-index(key, m0), 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, m1 / 2 < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ # mkkeyarray(n) = n; (s)% ⊦ m - 0 = m; (s)%m0 ≠ 0 ⊦ n ≤ m / m0 ↔ n * m0 ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ ¬ m < 0; (s)