I'd deal with it differently according to two separate cases.
Either way, first you need to get the the player to acknowledge that he keeps being proved wrong by the lookup, and he doesn't know his spells as well as he'd like, and the lookups are disruptive and undesirable. It might be that this is how he thinks the game should be played. It might be this is how his family played Monopoly, with lots of bluffing and arguing the rules, and demanding lookups, and that he enjoys it that way. So you need to explain that it isn't what you want in this campaign. It does not go without saying, that his behaviour is undesirable.
Your player is still learning, but you see progress
So, your player hasn't found time outside the game to properly read their character's spell list and so on. In most games that's allowed, but it's frustrating that this needs to happen in game time.
Explain that you're the DM, you know the rules pretty well, and that while you do make mistakes he should not always jump straight to assuming he's right and you're wrong over matters like the described effect of a particular spell. If he can't remember something then he should trust your memory (or other players at the table), and if he thinks you're wrong he should accept your ruling for the moment and look it up while the next action is being processed. If you absolutely need to in order to prevent him blocking play, offer that you will retcon in cases where he genuinely is right and you're wrong, and he can prove it by looking up the effect immediately after you demand that play move on (should any such cases occur -- you don't say he's ever been right yet so this is a small risk).
Suggest that if possible he find the time to re-read his own abilities more carefully (and new ones as he takes them), and if not he just accept that you've taken the time to learn this stuff and he hasn't, and he will best benefit from that by trusting you more than he is.
Suggest to him that he prints out or bookmarks his own spells/feats/etc for quick reference.
Your player doesn't respect the rules and is trying it on
A symptom of this would be that you find yourselves looking up the same spell effect over and over, because he makes the same wrong claims (or new wrong claims about the same thing) despite having been corrected by a lookup last time
In that case ultimately you need to call him out for problem behaviour. Regardless of what he's used to or prefers, in your game spells do what the rulebook says they do, not what is convenient for his character, or the drama of the scene, or whatever.
Start by pointing out, when it happens, that it's an undesirable delay. This might be enough to give him a better idea when (and how much) he's annoying you, and he'll self-regulate.
Failing that, explicitly ask for a change in his approach. Do this one to one in private. He needs to co-operate by paying attention to the relevant rules, and he needs to stop blocking the game when a disagreement occurs. Encourage him to ask you what a spell does if the details are important to his plan, not plan according to what he hopes it does and end up needing an argument. As and when he gives ground (for example accepting that he shouldn't do what he did), listen to what he's saying and bear that in mind. He'll quite likely surprise you at some point in the conversation: if he agrees immediately then don't stick to the things you planned to say when you assumed he'd take a lot of persuading because you'll be banging on needlessly.
General advice applies when calling someone out for misbehaviour -- talk about what he did, not what you believe his goals are or what you believe he thinks. Get your ducks in a row and don't accuse him of things that haven't happened. Don't accuse him of more than you need to in order to make your point (that is, don't "pile on" the charges). Don't get sidetracked into arguments about whether his way is better (or easier, or more fair) than what you expect from him. Remember you don't have to tell him (still less get him to agree) that what he was doing was wrong or inconsiderate, just that you want things done differently in your campaign.
Finally, as others have said, you would probably benefit from yourself being able to look this stuff up faster (by getting digital version of the rules or just practicing flicking through the books), or enlisting other players to help with that. If you could just short-circuit the arguments by finding the right page in under 30 seconds, then 2-3 instances of that per session is hardly the end of the world.