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Proof step 2 from proof prepost-resize (previous step)

bh0 = bh, bin-heap-inv(bh, ar) ⊦ ⟪bin_min_heap_resize#(minsize; bh)⟫ (bin-heap-inv(bh, ar) ∧ bh.size = bh0.size ∧ # bh.ar ≥ minsize ∧ subarray(bh.ar, 0, bh.size) = subarray(bh0.ar, 0, bh0.size))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
bh0 = bh, 2exp-size(# bh.ar), heap-order(bh.ar, bh.size), no-dups-idx(bh.ar, bh.size), valid-idx(bh.ar, ar, bh.size), bh.size ≤ # bh.ar ⊦ ⟪bin_min_heap_resize#(minsize; bh)⟫ ( 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 = bh0.size ∧ minsize ≤ # bh.ar ∧ subarray(bh.ar, 0, bh.size) = subarray(bh0.ar, 0, bh0.size))

Rule argument

Additional information

Used simplifier rules: bin-heap-inv-def: ⊦ bin-heap-inv(bh, ar) ↔ 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);% ⊦ n ≥ m ↔ m ≤ n; (s)