When I use the word "prove" i don't mean like proving things in math. Nobody means this, it's obvious to everyone what they mean. Prove in this context means well established. For example if I say scientists have proved the theory of gravity.
What's going on here is extreme pedantry. Prove has meaning in different contexts, you have chosen the most technical pedantic context to suit some misguided purpose rather than the most obvious context. There's no point in taking this further.