Sentence examples for a simple proof from inspiring English sources

A simple proof of this theorem was attributed to the Pythagoreans.

I offer a simple proof:Suppose an omniscient climatologist predicts that carbon-dioxide emissions will precipitate a crisis within five years.

We can give a simple proof.

See [20] for a simple proof.

A simple proof is given as following.

We give a simple proof of this conjecture.

Here we give a simple proof for the reader's convenience.

Here, we present a simple proof for this fact.

In this section, we formulate a simple proof.

We give a simple proof of this lemma.

Next, we give a simple proof for Theorem 1.3.