Building Proofs in Context

When reasoning with implicitly defined contexts or theories, a general notion of proof in context is more appropriate than classical uses of reflection rules. Proofs in a multicontext framework can still be carried out by switching to a context, reasoning within it, and exporting the result. Context switching however does not correspond to reflection or reification but involves changing the level of nesting of theory within another theory. We introduce a generalised rule for proof in context and a convenient notation to express nesting of contexts, which allows us to carry out reasoning in and across contexts in a safe and natural way.

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