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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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