Before revision:  A Prager-Synge type result relates the  errors of divergence-free primal and H( )-conforming dual mixed methods ( for the velocity gradient) with an equilibration constraint that needs special care when discretised.
After revision:  A Prager-Synge type result relates the errors of divergence-free primal and H( perfectly equilibrated dual mixed methods ( for the velocity gradient) with an equilibration constraint that needs special care when discretised.