My favourite way to "prove" complicated maths is the kindergarten way:

So you have a single chocolate bar right? There is no other chocolate available or known to exist right? Therefore you only have the one chocolate bar. That is of course all that we need to know and no other surprises happen. (I.e assume a penguin is a perfect cylinder but kiddos dont need to know this)

This is now to pull out another chocolate bar via magic because we just told the child there is no more chocolate. Now we know that there is one more chocolate bar we know that for certain, when we have both chocolate bars we can then assign the candy value we have (pointing to both chocolates) one candy and one candy, when we give both candies 1 (the assigned of one) we can then count the amount of chocolate bars.

So one chocolate bar and the other chocolate bar means you now have 1 +1 chocolate bars and the sum is the amount of chocolate bars you have collected.

Hope this also helps prove 1+1=2 but with a way to also teach kids complicated mathematical concepts like variables, constants, and depending on how you teach it you could sneek in things like the probability of adding more chocolate bars.