If Agnes's research proposal is approved, the fourth floor lab must be cleaned out for her use.
Conclusion
The 4th floor lab must be cleaned out.
If Agnes's proposal is approved, the 4th floor lab must be cleaned out. Only the proposals the director supports will be approved, and the director will support Agnes's proposal.
Evaluation
This might seem pretty valid at first, but whenever we're doing Flaw and we see conditional language, we should examine the directionality to make sure the author is thinking through it properly. The conditional trigger word here is "only", which always indicates the Necessary condition (right-side of the arrow).
Approved → Director Supports
The author is reasoning,
His reasoning looks like "Director Supports → Approved", so he is doing an Illegal Reversal of the conditional logic.
Goal
When authors mess up conditional logic, the fancy name for it is confusing Necessary with Sufficient (or vice versa). The informal way to object to it is to say,