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- \begin{tabular}{lll}
- $\hat{\theta}(c_0 \: (c_1 \: (c_1 \: c_2)))$ & = & $\lambda q.(q \: \lambda x \lambda y.(x + y)) \: ( \lambda q' \lambda f.(q' \lambda x' \lambda y'.(f \: (a + x' + b) \: (c + y' + d))) \: ( \lambda q'' \lambda f'.(q'' \lambda x'' \lambda y''.(f' \: (a + x'' + b) \: (c + y'' + d)))$ \\
- & & $ \lambda f''.(f'' \: \lambda i.(i) \: \lambda i'.(i'))))$ \\
- & $\rightarrow_\beta$ & $\lambda q.(q \: \lambda x \lambda y.(x + y)) \: ( \lambda q' \lambda f.(q' \lambda x' \lambda y'.(f \: (a + x' + b) \: (c + y' + d))) \: ( \lambda f'.(\lambda f''.(f'' \: \lambda i.(i) \: \lambda i'.(i'))$ \\
- \end{tabular}
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