that a row of pixels is not a tile as defined by the patent. On December 12, 2000, the district court issued an order which granted ERM's motion, and determined the meaning of the word "tile". On appeal, the Federal Circuit court reversed the grant of summary judgement and remanded for further proceedings, instructing the district court to consider the notion of "tile" to include a single row of pixels. On remand, the district court held that ERM did not infringe claims 1 or 13, based on a claim construction suggested by a special master. The district court also held that claim 21 was invalid for obviousness. Finally, the court held that claim 21 and its dependent claims (all the remaining claims) were invalid because they failed to satisfy the written description requirement of 35 U.S.C. § 112. LizardTech appealed each of the rulings. Opinion of the Federal Circuit court The Federal Circuit court affirmed the district court's judgement that ERM did not infringe claims 1 or 13, and that claims 21–25, 27 and 28 were invalid for failing to satisfy the written description requirement. They did not consider the district court's ruling that claim 21 was invalid for obviousness, since they had already decided it was invalid. Claims 1 and 13 Claims 1 and 13 contained a limitation related to "maintaining updated sums". The district court construed this limitation to mean "summing the DWT coefficients of one tile together with overlapping DWT coefficients from one or more adjacent tiles". Both parties agreed with this construction. The district court held that ER Mapper failed to meet the limitation, since it never added together overlapping DWT coefficients. LizardTech argued that the district court's holding changed the definition of "overlapping", and therefore altered their original construction of the claim which LizardTech had agreed to. The district court disagreed, saying that within the context, overlapping "can only mean that the DWT coefficient ... obtained from the data in one tile, is added to the DWT coefficient at the same position, obtained from the data in an adjacent tile". LizardTech then argued that in the district court's construction, if DWT coefficients were generated from adjacent tiles, then they necessarily "overlapped". The district court rejected the argument, saying that the ER Mapper program calculated DWT coefficients only within the current tile. Finally, LizardTech argued that after ER Mapper calculated the DWT of the image rows,