True, but testing is not about correctness proving, it is about checking to see if something seems to behave correctly .
Also worth noting: proving something correct does not actually mean it will then seem to behave correctly, if you have misconceived the application of what you have proven correct.
I don't test what I write as much as I should (because I enjoy debugging later so much) but I did read somewhere that "studies have shown" that the number of bugs found in say 10 poorly tested units over the next 6 months will be much higher than those found in 10 similar but well tested units, even if the exact same people wrote all the code -- regardless of whether anything is "proven correct" in the process.