A finite event will be said to extend throughout a duration when it is part of the duration and is intersected by any moment which lies in the duration.

Such an event begins with the duration and ends with it.

Furthermore every event which begins with the duration and ends with it, extends throughout the duration.

This is an axiom based on the continuity of events.

By beginning with a duration and ending with it, I mean (i) that the event is part of the duration, and (ii) that both the initial and final boundary moments of the duration cover some event-particles on the boundary of the event.
Every event which is cogredient with a duration extends throughout that duration.
It is not true that all the parts of an event cogredient with a duration are also cogredient with the duration.