  In this paper, we utilize Isabelle/HOL to develop a formal framework for the
basic theory of double-pushout graph transformation. Our work includes defining
essential concepts like graphs, morphisms, pushouts, and pullbacks, and
demonstrating their properties. We establish the uniqueness of derivations,
drawing upon Rosens 1975 research, and verify the Church-Rosser theorem using
Ehrigs and Kreowskis 1976 proof, thereby demonstrating the effectiveness of our
formalisation approach. The paper details our methodology in employing
Isabelle/HOL, including key design decisions that shaped the current iteration.
We explore the technical complexities involved in applying higher-order logic,
aiming to give readers an insightful perspective into the engaging aspects of
working with an Interactive Theorem Prover. This work emphasizes the increasing
importance of formal verification tools in clarifying complex mathematical
concepts.
