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That plans work in urban development is a claim that lacks theoretical and empirical backing. In the present paper, we consider the urban development process as a set of five partially independent streams of problems, solutions, decision makers, locations, and decision situations. When the elements of the five streams collide under some structural constraints and fulfill an energy surplus decision rule, decisions are made. Given this model of urban development in which plans and the planner are embedded, we prove axiomatically that some characteristics of urban development decisions, namely interdependence, indivisibility, irreversibility, and imperfect foresight, or the four I's, are the sufficient condition for the complexity of the city, and that the four I's in turn are the necessary condition for why plans work. The two lemmas together give rise to the theorem that plans work in the face of complexity as manifested by the urban development process. The theorem reached from the axiomatic system provides a theoretical basis on which planning is practiced in the face of complexity and the results might prompt us to return to and focus on plans as the object in planning research.