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Theorem bubble-up

bin_min_heap_bubble_up#(n; bh, ar) {let m = n in while m ≠ 0 ∧ bh.ar[m].key < bh.ar[(m - 1) / 2].key do let ki = bh.ar[m], ki0 = bh.ar[(m - 1) / 2] in {bh.ar[m] := ki0; ar[ki0.idx].idx := m; m := (m - 1) / 2; bh.ar[m] := ki; ar[ki.idx].idx := m} }