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[ { "from": "human", "value": "Add some simple logic inductive types for testing\n" }, { "from": "gpt", "value": "module Logic\n\ninductive True : Type\n | I : True\nend\n\ninductive False : Type\nend\n\ndef not (P : Type) : Type :=\n P -> False\nend\n\ninductive And (P : Type) (Q : Type) : Type\n | Conj : P -> Q -> And P Q\nend\n\ninductive Or (P : Type) (Q : Type) : Type\n | OrIntroL : P -> Or P Q\n | OrIntroR : Q -> Or P Q\nend\n\ndef main : True := I end\n" } ]
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