Quillen stratification for the Steenrod algebra

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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 Extₐ (Z/2,Z/2) --> Extₑ (Z/2,Z/2), for E in Q, can be assembled into a map i:Extₐ (Z/2, Z/2) --> limQ Extₑ (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:Extₐ (Z/2, Z/2) --> (limQ Extₑ (Z/2,Z/2))ᵃ. We show that g is an F-isomorphism.