Actually I couldn't understand a thing you were trying to say.
I can't "prove" anything. This isn't an issue where there's going to be 100% proof of anything. To ask such a question is to show lack of understanding of the issues.
One of the biggest issues with gun crime is the availability of guns to criminals.
So what I'll do is present some things, and then you can look at the argument I'm making and you can try and pick holes in it, okay?
Comparison of international gun homicides.
List of countries by firearm-related death rate - Wikipedia
The US has a gun homicide rate of 4.46
The UK has a gun homicide rate of 0.06
Switzerland has a gun homicide rate of 0.15
Now, Switzerland has a lot of guns, but also has strict laws on how you keep guns, so guns aren't actually that easily available to criminals. Whereas in the US they are. They on'y have a rate of 27 guns per 100 people, compared to 120 for the US.
England and Wales has a rate of 4.6 guns per 100 people.
Germany, has a higher gun murder rate than Switzerland with 19.6 guns per 100 people and a gun murder rate. Germany has a rate of about 1 per 100,000 for gun murders.
So, the factors we're looking at here are easy availability of guns. Not numbers of guns. In the US guns are so easy to get. In Switzerland they're difficult because of the laws. In Germany they're easier to get hold of and gun murders increase.