Flying squadron tutored madmen that needed proving (4,4,13)

I believe the answer is:

quod erat demonstrandum

I'm a little stuck... Click here to teach me more about this clue!

'flying squadron tutored madmen that needed proving' is the definition.
The definition suggests a singular noun which matches the answer.

'flying squadron tutored madmen that needed' is the wordplay.
'flying' indicates an anagram (letters fly around into new positions).
'that needed' is a charade indicator (letters next to each other).
'squadron'+'tutored'+'madmen'='squadrontutoredmadmen'
'squadrontutoredmadmen' with letters rearranged gives 'QUOD ERAT DEMONSTRANDUM'.

Can you help me to learn more?

(Another definition for quod erat demonstrandum that I've seen is " I was trying to show that".)

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.