Background: In model-driven development, model transformation transforms one model to another between different phases of software engineering. In model transformation, metamodel plays a vital role which defines the abstract syntax of models and the interrelationship between their elements. A unified metamodel defines an abstract syntax for both source and target models when they share core elements. Theoretical approaches define language and platform independent representation of models in software engineering. This paper investigates the theoretical foundation to this unified meta-modelling for their consistent transformation. Objective: This paper aims to define the formal foundations to the unified metamodel for generating implementation from design specifications and model reusability. Method: In this paper, the study considers transformation from design to implementation and vice versa using theoretical foundations to build a verified software system. Results: The related tools provide a formal representation of the design phase for verification purpose. Our approach provides a set-theoretical foundation to the unified metamodel for model transformation from USE (UML/OCL) to Spec#. In other words, our approach defines the formal foundation to define a model which consists of all the required properties for verification at the design and implementation phase. Conclusion: This paper introduced a new set of the theoretical framework which acts as an interface between the design and implementation to generate verified software systems.