  Software is now ubiquitous and involved in complex interactions with the
human users and the physical world in so-called cyber-physical systems where
the management of time is a major issue. Separation of concerns is a key asset
in the development of these ever more complex systems. Two different kinds of
separation exist: a first one corresponds to the different steps in a
development leading from the abstract requirements to the system implementation
and is qualified as vertical. It matches the commonly used notion of
refinement. A second one corresponds to the various components in the system
architecture at a given level of refinement and is called horizontal.
Refinement has been studied thoroughly for the data, functional and concurrency
concerns while our work focuses on the time modeling concern. This contribution
aims at providing a formal construct for the verification of refinement in time
models, through the definition of an order between strict partial orders used
to relate the different instants in asynchronous systems. This relation allows
the designer at the concrete level to distinguish events that are coincident at
the abstract level while preserving the properties assessed at the abstract
level. This work has been conducted using the proof assistant Agda and is
connected to a previous work on the asynchronous language CCSL, which has also
been modelled using the same tool.
