Maintain an integer len, initially zero, with len = length xs:
PROCEDURE Add(x: INTEGER);
BEGIN
  ASSERT(len < N);
  u[len] := x;
  len := len+1
END Add;
The precondition is the abstract capacity condition. Appending at the first unused array index establishes in constant running time.
If get(k) first applies a comparison sort to all entries, the comparison sorting lower bound gives at least comparisons in the worst case. A merge sort or heapsort meets that order, after which indexing costs constant time:
(1)
This is a logarithmic factor worse than linear. The qualification to comparison sorting is necessary: merely saying that keys are integers does not prohibit counting sort for a bounded small range or radix sort under suitable machine-key assumptions. The printed assertion of an unavoidable superlinear bound needs the comparison model.

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