The purpose of this note is to give a brief and clear description of an inequality with applications in computer graphics, including a sketch of the proof. Difficulties related to the formulation and to the proof of the inequality are due to the rather complicated order condition. A complete proof and a detailed description of the application are given in [1]. Roughly speaking, if the merging of two disjoint non-decreasing sequences, which consist of non-negative integers and have the same length, determines at most $h+1$ maximal subsequences of the input sequences, and if the sums of the $r$-th powers of the members are the same with the both sequences for $1\leq r\leq h-1$, then the sum of the $h$-th powers is greater with the sequence which contains the largest integer of the merged sequence.