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Proof step 17 from proof prepost-resize (previous step)

kar0 = mkkeyarray(n0), 2exp-size(# kar), 2exp-size(n0), m < n0, m < minsize, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0, 0 + m ≤ # kar0, 0 + m ≤ # kar ⊦ bin-heap(copy(kar, 0, kar0, 0, m), m).size ≤ # bin-heap(copy(kar, 0, kar0, 0, m), m).ar ∧ no-dups-idx(bin-heap(copy(kar, 0, kar0, 0, m), m).ar, bin-heap(copy(kar, 0, kar0, 0, m), m).size) ∧ valid-idx(bin-heap(copy(kar, 0, kar0, 0, m), m).ar, ar, bin-heap(copy(kar, 0, kar0, 0, m), m).size) ∧ 2exp-size(# bin-heap(copy(kar, 0, kar0, 0, m), m).ar) ∧ heap-order(bin-heap(copy(kar, 0, kar0, 0, m), m).ar, bin-heap(copy(kar, 0, kar0, 0, m), m).size) ∧ bin-heap(copy(kar, 0, kar0, 0, m), m).size = m ∧ minsize ≤ # bin-heap(copy(kar, 0, kar0, 0, m), m).ar ∧ subarray(bin-heap(copy(kar, 0, kar0, 0, m), m).ar, 0, bin-heap(copy(kar, 0, kar0, 0, m), m).size) = subarray(kar, 0, bin-heap(copy(kar, 0, kar0, 0, m), m).size)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
2exp-size(n0), 2exp-size(# kar), m < minsize, m < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦ no-dups-idx(copy(kar, 0, mkkeyarray(n0), 0, m), m) ∧ valid-idx(copy(kar, 0, mkkeyarray(n0), 0, m), ar, m) ∧ heap-order(copy(kar, 0, mkkeyarray(n0), 0, m), m)

Rule argument

Additional information

Used simplifier rules: m1 + n ≤ # kar ⊦ subarray(copy(kar0, m0, kar, m1, n), m1, n) = subarray(kar0, m0, n); (s)% ⊦ # copy(kar, m, kar0, m0, n) = # kar0; (s)% ⊦ bin-heap(kar, m).ar = kar; (s)% ⊦ bin-heap(kar, m).size = m; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ # mkkeyarray(n) = n; (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)