How do we proof that its really that difficulty

If you are talking about UV or higher, you show the menu at the start of the run like it says in rules.

You can also tell by what's happening in the run.

Double ammo pickup, easy enemy spawns = ITYTD Easy spawns = HNTR Normal spawns = Hurt me Plenty Hard Spawns = Ultra-Violence Co-op spawns = UV+ Fast enemies, respawns... surely, you can recognize Nightmare.

Plus, I'm pretty sure the damage you take from enemies also differs between difficulties.

Only ITYTD has different damage taken from the rest, 50% less.

alright thanks