Equality of agent expressions is preserved under an extension of the universe of actions

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Abstract In a basic agent calculus, equality often links the agents which provide the same external behaviour in any context. Since the universe of agents and the universe of contexts depend on the used action set, equality depends a priori on this set of actions. We show here that if we select from the universe of agents, two agents which are equal, they are also equal if we extend the universe of actions (and consequently if we extend the universe of agents and contexts).