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Proof step 8 from proof prepost-resize (previous step)

bh = bin-heap(kar, m), n = # bh.ar, 2exp-size(# kar), minsize > bh.size, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ ⟪bin_min_heap_next_2pot(minsize; n); let kar = mkkeyarray(n) in {kar := copy(bh.ar, 0, kar, 0, bh.size); bh.ar := kar}⟫ ( 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 9:
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); 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: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ bin-heap(kar, m).ar:= kar0 = bin-heap(kar0, m); (s)% ⊦ m > n ↔ n < m; (s)% ⊦ bin-heap(kar, m).size = m; (s)% ⊦ bin-heap(kar, m).ar = kar; (s)