Proof comes from a premise or premisses and an argument. For instance:
(1) All cats have fur.
(2) Fluffy is a cat.
(3) If Fluffy is a cat, then Fluffy has fur.
(1) and (2) are premisses. (3) is an argument. If the premisses are true and the argument is reasonable, we have proof that Fluffy has fur.
The problem usually is trying to establish that your premisses are true. Events occur in time. To actually say that an event happened requires evidence of its occurance. Evidence can be eyewitness accounts and the current effects of the event's occurance. For instance we may have:
(A) A live, furless cat with a collar bearing the name tag "Fluffy."
(B) a pile of white curly hair near the cat.
(C) a hair clipper.
(D) a 10 year old boy with bleeding scratches all over his forearms. He denies having shaved the fur off the cat.
(E) a 7 year old girl who claims to have seen the boy shaving the fur off the the cat.
(F) finger print the boy. We lift finger prints off of the clipper. They match.
(G) call in a veterinarian. She says the scratches on the boy's are are consistant with the scratches that the cat could have made.
(H) test the blood on the cat's claws. The DNA of the blood on the cat's claws matches the boy's DNA.
(I) test the DNA of Cat. The DNA of the pile of curly hair on the floor matches the cat's DNA.
Items (A) through (I) are evidence. But until someone puts together a logical, inductive argument using the evidence as premisses, there's no proof that Fluffy ever had any fur or that the boy shaved it off.