  We give a constructive account of the de Groot duality of stably compact
spaces in the setting of strong proximity lattice, a point-free representation
of a stably compact space. To this end, we introduce a notion of strong
continuous entailment relation, which can be thought of as a presentation of a
strong proximity lattice by generators and relations. The new notion allows us
to identify de Groot duals of stably compact spaces by analysing the duals of
their presentations. We carry out a number of constructions on strong proximity
lattices using strong continuous entailment relations and study their de Groot
duals. The examples include various powerlocales, patch topology, and the space
of valuations. These examples illustrate the simplicity of our approach by
which we can reason about the de Groot duality of stably compact spaces.
