I am trying to prove the tautology ((P->Q)xP)->Q in type theory, and I can't quite get started. Any help would be great.
Proving a tautology in type theory
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type-theory
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1What notation is that? What does the "x" mean? – 2017-02-02
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0@Wildcard I assume it's supposed to be a $\times$, so that the whole type he wants to inhabit is $((P \to Q) \times P) \to Q$. – 2017-02-02
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Consider the term \begin{align*} \lambda \operatorname{pair} : (P \to Q) \times P . (\operatorname{proj}_1 \operatorname{pair}) (\operatorname{proj}_2 \operatorname{pair}) \end{align*} where $\operatorname{proj}_1$ and $\operatorname{proj}_2$ are the first and second projections of the Cartesian product "$\times$", respectively.