Ukraine

It's hard to say, that it's prooved. Probably even the US Ministry of Defence has no totaly exact lists.

But there are good estimations based on reports and leaked footage.

For example oryx has a list with destroyed vehicles and equipment based on photographic or videographic evidence. The real numbers are probably significantly higher.

After this list the russian army lost more than 2000 tanks. Ukrainian sources says that the Invasion started with more than 3000 tanks.

Ca. 1000 of the 2000 lost tanks were T-72 (the most common tank in the russian army). According to estimations russia has 2000 T-72 in active service and maybe 10.000 or more as reserves. The reserves are mostly remnants of the soviet Union and old models that are never modernized. Satellite pictures show that a big part of this reserves are stored in open depots with no weather protection. Maybe russia could make some of this vehicles usable, it will cost Billions to repair and modernize them.

So, no there is no proof, that the ukrainian army destroyed 50% of the russian forces. But there are proofs that russia lost a significant part of its active forces (probably something close to this claim) and that they definitly lost much more value than the americans, the europeans, ect. invested in the ukrainian army.

https://www.oryxspioenkop.com/2022/02/attack-on-europe-documenting-equipment.html?m=1

https://inews.co.uk/news/world/tanks-russia-how-many-putin-military-ukraine-leopard-2-abrams-2108097

https://en.m.wikipedia.org/wiki/T-72