We can prove mathematical statements with a method involving contradictions. The premise is simple (the steps not so much). For a given statement, we assume that it’s not true (or alternatively that the inverse is true). We then work through steps that eventually conclude in something that contradicts our assumption, thus proving the statement.
i.e., every step we did was correct or logically sound. Thus, the initial assumption must be false.
”ATaC” means “assume towards a contradiction”.