[Doctor Stochastic]

Correct. You may call the mean value theorem valid, but you cannot call it "true." You may wish to read an introductory book on the foundations of mathematics for an elucidation of this point. Proofs are valid or invalid, not true or false.

[Dr. Frank fan]

You may call the mean value theorem valid, but you cannot call it "true."

Sigh, I've been arrested by the self-anointed semantical police again....

Listen: I reject your statement. The mean value theorem is true, and its proof is also true.

If you're still confused, keep in mind that here, I am using the word "true" as would an ordinary English speaker. That is because I am participating on an American political discussion board. I don't know where you think you are.

[Dr. Frank fan]

P.S. "2+2=4" is also true, according to the way I (but not you) am using "true". The reader may decide for him/herself whose usage of the word is more appropriate for political discussion.