Abstract: We introduce, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true over some relevant collections of instances and false over some relevant collections of instances. A rigorous, algorithmic criterion is presented for detecting such cases, and its performance is exemplified through the implementation of this test within the dynamic geometry program GeoGebra. Our framework has some significant differences regarding some alternative, recent formulation of the ?true on components? idea; differences and similarities between both approaches are discussed here.

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