Just because i wanted, not that your "logic" is logical. its could be called bullshitology. But lets take your v&v&v&v&v&v you say is 6 check marks. Wel in math thats not true.

Because in math any symbol that is not a number and not a calculation symbol represents something else. So that string is then mathematically 5V&+V. unless you use & as representing +. it its 6V.

And if one is to use your logic that indicates 0 to have a value of 1. then any number in a additive calculation needs a +1 meaning 2+2=6. and that would only cause unnecessary confusion to a function logical math bases that already exist.

In conclusion: no, you cannot prove that 2+2=5. the only way it can be said that you do, is if you can also prove that a circle is a square, a computer is a horse, that 1-1=50. by making up any bad yet good sounding logic to explain it. Just like convincing politicians do.
or like many also call it: trolling