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The concept of "Is the useless one useless?"

For example, there is a theorem.
"If A, then B."
This is the theorem. So, "If not A, then it is not sure B or not."
Do you think it is not remarkable "if not A"?
"Is the useless one useless?"
Are there anything interesting related to that?
This is the concept of this section.

Forum of Geometric Constructor by Y.Iijima