  We present a first-order linear-time temporal logic for reasoning about the
evolution of directed graphs. Its semantics is based on the counterpart
paradigm, thus allowing our logic to represent the creation, duplication,
merging, and deletion of elements of a graph as well as how its topology
changes over time. We then introduce a positive normal forms presentation, thus
simplifying the actual process of verification. We provide the syntax and
semantics of our logics with a computer-assisted formalisation using the proof
assistant Agda, and we round up the paper by highlighting the crucial aspects
of our formalisation and the practical use of quantified temporal logics in a
constructive proof assistant.
