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If a section heading arrives at the end of a page, and there is no more space to include the later text body, the section heading will be shifted to the next page (the section, subsection, ..., all have this property, by default).

Now, I want to define a new section-like environment. This environment has a red line below of its heading and we can insert our text underneath this line.

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Why does it need to be a new environment? The titlesec package for instance lets you configure section titles. – Stephan Lehmke Dec 13 '12 at 22:11
Perhaps this answer to tex.stackexchange.com/q/86825/3954 can be useful in this situation. – Gonzalo Medina Dec 13 '12 at 23:17

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