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Proof step 11 from proof prepost-resize (previous step)

minsize0 = minsize, n = # kar, 2exp-size(# kar), 2exp-size(n), m < minsize, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ [bin_min_heap_next_2pot(minsize; n)] ( 2exp-size(n) ∧ n ≥ minsize0 → ⟪let kar0 = mkkeyarray(n) in {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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n = # kar, 2exp-size(# kar), m < minsize, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ [bin_min_heap_next_2pot(minsize; n)] ( 2exp-size(n) ∧ minsize ≤ n → ⟪let kar0 = mkkeyarray(n) in {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)))

Rule argument

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)