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Theorem build-rec

build_rec# (d; x, to) { if is_empty(x) then to := fail else let h = head(x) in if h < d then to := fail else if h = d then { x := pop(x) ; to := some(Leaf) } else let to0 = fail, to1 = fail in { build_rec#(d + 1; x, to0) ; if to0 = fail then to := fail else { build_rec#(d + 1; x, to1) ; if to1 = fail then to := fail else to := some(Node(to0 .t, to1 .t)) } } }