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Proof step 15 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 ⊦ ⟪kar0 := copy(kar, 0, kar0, 0, m); bh := bin-heap(kar0, m)⟫ ( bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) ∧ bh.size = m ∧ minsize ≤ # bh.ar ∧ subarray(bh.ar, 0, bh.size) = subarray(kar, 0, bh.size))

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 16:
kar0 = mkkeyarray(n0), 2exp-size(n0), 2exp-size(# kar), m < minsize, m < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), 0 + m ≤ # kar, 0 + m ≤ # kar0, minsize ≤ n0, m ≤ # kar ⊦ ⟪bh := bin-heap(copy(kar, 0, kar0, 0, m), m)⟫ ( bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) ∧ bh.size = m ∧ minsize ≤ # bh.ar ∧ subarray(bh.ar, 0, bh.size) = subarray(kar, 0, bh.size))

Rule argument

Additional information

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