where formula_67 is an Eilenberg–MacLane space. We then further convert the map formula_68 to a fibration; it is general knowledge that the iterated fiber is the loop space of the base space so in our example we get that the fiber is formula_69 But we know that formula_70 Now we look at the cohomological Serre spectral sequence: we suppose we have a generator for the degree 3 cohomology of formula_71, called formula_72. Since there is nothing in degree 3 in the total cohomology, we know this must be killed by an isomorphism. But the only element that can map to it is the generator "a" of the cohomology ring of formula_73, so we have formula_74. Therefore by the cup product structure, the generator in degree 4, formula_75, maps to the generator formula_76 by multiplication by 2 and that the generator of cohomology in degree 6 maps to formula_77 by multiplication by 3, etc. In particular we find that formula_78 But now since we killed off the lower homotopy groups of "X" (i.e., the groups in degrees less than 4) by using the iterated fibration, we know that formula_79 by the Hurewicz theorem, telling us that formula_64