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Formalized: Intuitionistic Propositional Calculus (IPC) plus Atomic Law of the Excluded Middle (ALEM) is Classical Propositional Calculus (CPC)

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IPC + ALEM = CPC formalized in Coq

First, the basic logical notions such as the definition of formulas are formalized. Then the natural deduction system plus the axiom scheme of The Law of the Excluded Middle but only for atomic formulas (ALEM) is defined and a single theorem shows that permuting, condensing or eliminating repetitions in a context does not affect the derivable formulas in that context. Following that, using induction on the complexity of formulas we derive the general law of the excluded middle and conclude: IPC + ALEM = CPC.

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Formalized: Intuitionistic Propositional Calculus (IPC) plus Atomic Law of the Excluded Middle (ALEM) is Classical Propositional Calculus (CPC)

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