### Abstract

Economic activity has always been a fundamental part of society. Due
to modern day politics, economic theory has gained even more influence
on our lives. Thus we want models and theories to be as precise as
possible. This can be achieved using certification with the help of
formal proof technology. Hence we will use Isabelle/HOL to construct
two economic models, that of the the pure exchange economy and a
version of the Arrow-Debreu Model. We will prove that the

GNU Lesser General Public License (LGPL)*First Theorem of Welfare Economics*holds within both. The theorem is the mathematical formulation of Adam Smith's famous*invisible hand*and states that a group of self-interested and rational actors will eventually achieve an efficient allocation of goods and services.### Change history

[2018-06-17] Added some lemmas and a theory file, also introduced Microeconomics folder.