In this case, the string is it proved is a subject-auxiliary inversion of it is proved, which is a combination of dummy it with the simple passive is proved. The dummy subject it is inserted during extraposition, taking the place of the content clause, which is moved to the end of the sentence:
[That X is true] is proved. → It is proved [that X is true].
We can contrast the simple is proven with the perfect has been proved:
[That X is true] has been proved. → It has been proved [that X is true].
There's one complication: this particular verb has two past participles, proved and proven. That means we can write any of the following:
simple passive perfect passive
--------------------- -------------------------
It is proved It has been proved
It is proven It has been proven
All of these are grammatical, and the proved and proven versions are equivalent. The real question isn't proved versus proven, but simple versus perfect. Even though both versions are grammatical, they aren't used in the same situations. The simple version is used when I am talking about where something is proved, in a conditional, or (rarely) if something is proved right now.
- "Where is the theorem proved?" "It is proved in Appendix B."
- "If and when the theory is proven, you'll get your grant money."
- "It will be proved in five seconds. Five. Four. Three. Two. One. It is proven." (spoken, rare)
The perfect version is used when you're talking about something proved in the past, or whether something has been proven in the past:
- "I'm not sure if this is a good idea." "Don't worry, it's been proven to work."
- "The Theory of Evolution has been proven."
- "Has it been proved that the United States didn't have a third atomic bomb to drop over Japan?"
Note that outside of this context, proved and proven aren't always equivalent. Proven is favored in attributive uses (a proven fact, not *a proved fact) and in certain set phrases (innocent until proven guilty). The preterite is always proved, not proven (I proved him wrong, but never *I proven him wrong).
In this case, I agree with the edit. The change to proven is perhaps unnecessary, but to my ear it sounds better, so I don't object to that, either. Has it been proved would also be fine.
Both are used and both are acceptable, though you are most likely to hear "that's" rather than "that is/was".
However, "is" cannot be used if the reason, per se, happened in the past.
'Remember when you got an F?'
'Yes. That was because I couldn't find my homework because you hid it.'
Best Answer
If the text was a quote from a book, then perhaps one could argue that it's a stylistic turn of phrase, but didn't have any thought left is certainly not idiomatic in English.
If the implication is that she has no actual thought on the matter (either she didn't care any more, or she no longer had the strength to think about it), something along the lines of
...might be more idiomatic.
One could also use a similarly worded idiom - to draw a blank - to imply that she was trying to think of something but couldn't.