conclusively

In a conclusive manner; with finality; decisively.

Once the final experiment had been performed, the theory was conclusively proved.

I need not extend the subject any farther; enough has been said , and much more might be, if necessary, to prove clearly and conclusively that the odontotechny of the Greeks and Romans was advanced to a considerable degree of perfection: […]

By way of conclusion.

"Go and find out who did it, before you come blaming me for it." "It's only youse crowd wot comes makin' a pigsty of the place," said Melons conclusively. "It ain't the second nor third floors wot comes makin' all manner o' mess in these basins."