Quillen stratification for the Steenrod algebra

Let A be the mod 2 Steenrod algebra, and let Q denote the category of exterior sub-Hopf algebras of A, where the morphisms are given by inclusions. The restriction maps Ext_A (Z/2,Z/2) --> Ext_E (Z/2,Z/2), for E in Q, can be assembled into a map i:Ext_A (Z/2, Z/2) --> lim_Q Ext_E (Z/2,Z/2). There is an action of A on this inverse limit, and i factors through the invariants under this action, giving a map g:Ext_A (Z/2, Z/2) --> ( lim_Q Ext_E (Z/2,Z/2) )^A. We show that g is an F-isomorphism.