What tells us that mammoths lived at the same time as people?

Scientists have proven that mammoths lived the same time as humans by finding fossils by each other ( human and mammoth fossils.) then doing dating tests to see if they're the same number of years old. And yes indeed fossils of humans and mammoths have been found that have been alive the same year as each other. This also proves that humans lived in the time of the ice age.

There are also mammoth bones that have been cut by spears and by stone knives.

There are also many examples of cave drawings of the woolly mammoth and carbon dating of fossils show them to have been around as recently as 9,000 years ago.

Am I the only one here who has access to google? :)