no proof   (証明なし)

Lamer said that there was no proof of this interpretation.

There is however no proof of this.

But the Sages said that no proof can be brought from a carob tree.

burden of proof   (立証責任)

The burden of proof is on the franchisee.

The burden of proof is on the person making a contentious claim.

The third and final principle concerns the burden of proof with respect to self-defense.

proof of concept   (コンセプトの証明)

SWIFT has deployed a proof of concept using Solidity running on Burrow.

Their initial proof of concept was a program that allowed users to search for flights using their voice.

After the proof of concept, the long-term goal of NASA is to transfer the technology to the commercial sector.

further proof   (さらに証明)

The latter, according to "Variety", is "further proof of Romania's new prominence in the film world."

Among his first-round victories was also a one-punch-knockout, a further proof of his outstanding punching power.

They also mention that a complete absence of air bubbles in the rock slabs is further proof that the specimen is authentic.

provide proof   (証拠を提供する)

All prospective members must provide proof of their Orthodoxy with their application.

These qualifications provide proof of the successful candidate’s proficiency in English.

For these seats, a student needs to provide proof by using their related certificate to authority.

without proof

The general result is taken here without proof.

Theorems are often presented without proof.

He made the assertion known as Waring's problem without proof in his writings "Meditationes Algebraicae".