Event Universes: Specification and Analysis Using Coq Proof Assistant Grygoriy Zholtkevych [0000-0002-7515-2143] School of Mathematics and Computer Science V.N. Karazin Kharkiv national University, 4, Svobody Sqr., Kharkiv, 61022, Ukraine g.zholtkevych@karazin.ua Abstract. In the paper, the formal specification of event universes the- ory developed with using Coq Proof Assistant is presented. The main attention is paid on the discussion of the definition and obtained facts. In the same time, a proof technique is not the subject of this discussion. The reader can get acquainted with the details of the proof technique, referring to the source text of Coq-scripts hosted on the GitHub, using the links provided in the text of the paper. Keywords: causality relationship· Calculus of Inductive Constructions· Coq Proof Assistant· decidability· class type· Category Theory 1 Introduction Inception of distributed computation technology has posed a problem of orches- tration of different computational device operating. One of the key problem in this context is to ensure adequate responses of a computational device involved into the computation to requests of other computational devices involved into the computation too in order to ensure all these computational devices behave consistently and purposefully. Thus, it is needed to give system developers tools for specification and analysis of timing constraints for ensuring the consistent behaviours of hardware and software constituted the system being under design. Hence, we may claim that carefully vetted specification guaranteeing the system behaviour consistency in the time is the important part of a good design for a distributed system. The specificity of the design process for distributed systems is the impos- sibility to apply the methods of dynamic analysis of program code to ensure its correctness. The reason for the validity of this claim is that any additional observations of the system are not possible without inclusion into the system special components, which collect the needed information but at the same time these components change the system behaviour. In some sense, we have be- haviour like quantum behaviour: any observation changes essentially the system behaviour. In the situation when dynamical analysis of the system correctness is not useful, the static analysis remains the unique method for assessment of system behaviour correctness. Thus, the creation of a rigorous theory, which