Examples play a variety of roles in proving and disproving. Buchbinder and Zaslavsky (2019) have produced an a priori mathematical framework for assessing students' understanding of the role of examples when proving and disproving universal and existential statements. In this paper, I highlight three important aspects that suggest an extension of Buchbinder and Zaslavsky's framework. These aspects arose a posteriori from research that had a focus on developing mathematically aligned assumptions related to proof and proving. To better approach students' understanding of the role of examples in proving and disproving, these three aspects need to be explicitly included in the framework: (1) the "size of the domain" where universal and existential statements are defined, (2) the "different forms of expression" in which universal and existential statements can be presented, and (3) the "quality" of universal and existential statements. Illustrations of the development of in-service primary school teachers' assumptions are given to show the emergence of these aspects and to support the extension of the existing framework.