Four distinct types? It's six!

Should "four" be corrected as "six"?

Context:

Thus ALPS has been classified into four distinct types: ALPS 0 (deficiency of Fas caused by homozygous null mutations); ALPS Ia (heterozygous Fas gene mutation); ALPS Ib (heterozygous Fas ligand gene mutation); ALPS IIa (caspase-10 gene mutation); ALPS IIb (caspase-8 gene mutation); and ALPS III (mild clinical features, no mutation identified).