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. To relax the constraints on the primal and dual method , a more general result is derived that enables the use of a recently developed mass conserving mixed stress discretisation to design equilibrated fluxes that yield pressure-independent guaranteed upper bounds for any pressure-robust ( but not necessarily divergence-free) primal discretisation.
After revision:  A Prager-Synge type result relates the errors of divergence-free primal and H( )-conforming dual mixed methods ( for the velocity stress. The first main result of the paper is a framework with relaxed constraints on the primal and dual method , a more general result is derived that enables the use of a recently developed mass conserving mixed stress discretisation to design equilibrated fluxes that yield pressure-independent guaranteed upper bounds for any pressure-robust ( but not necessarily divergence-free) primal discretisation.