proofs

the lawyer presented compelling proofs to support his client's innocence.

mathematical proofs are essential for establishing the validity of a theorem.

she meticulously gathered evidence and proofs to build her case.

the detective sought concrete proofs to solve the mystery.

providing solid proofs is crucial in a legal setting.

the scientist needed experimental proofs to support her hypothesis.

we examined the available proofs carefully before making a decision.

the company's claims lacked sufficient proofs to convince investors.

he challenged her to provide proofs of her accusations.

the historical proofs supported the archaeologist's theory.

the student struggled to understand the complex proofs in the textbook.

the judge requested further proofs to clarify the situation.