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Theorem remove

bin_min_heap_remove#(n; bh, ar) {if ¬ n < bh.size then abort; bh.size := bh.size - 1; if bh.size ≠ 0 ∧ bh.size ≠ n then {bh.ar[n] := bh.ar[bh.size]; ar[bh.ar[n].idx].idx := n; if n ≠ 0 ∧ bh.ar[n].key < bh.ar[(n - 1) / 2].key then bin_min_heap_bubble_up#(n; bh, ar) else bin_min_heap_bubble_down#(n; bh, ar)} }