Spatial data types provide a fundamental abstraction for modelling the geometric structures of objects in space, their relationships, properties and operations. In this work, we present a formal specification and verification of spatial data types with the B-Toolkit. We give a formal specification of a realm and operations over it using Abstract Machine Notations (AMN) of B. We then refine and implement a realm update operator in B, and verify formally an implementation of a realm update operator with B-Toolkit.