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Strengthened mere choice
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@@ -110,8 +110,7 @@ Section structure_k_finite.
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intros.
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destruct X0 as [SX EX].
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rewrite EX.
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simple refine (Trunc_ind _ _ (merely_choice SX)).
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intros [SXE | H1].
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destruct (merely_choice SX) as [SXE | H1].
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- rewrite SXE.
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apply (tr (inl idpath)).
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- apply (tr (inr H1)).
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