There's no rigorous proof one way or the other.

See the article on Ramsey's theorem for a rigorous proof.

However, the first mathematically rigorous proof of this fact was obtained only in the 19th century.

This outline should not be considered a rigorous proof of the theorem.

This article was the first to provide a rigorous proof that there was more than one kind of infinity.

And when was the last time that you had to subject your hypotheses to the test of rigorous proof by experiment, eh?

For a rigorous and general proof, see Kelly's original paper or some of the other references listed below.

A rigorous proof of this inequality was not given until 1948 by Pólya.

The rigorous proof of the solution can be found in references of their work.

Again, a rigorous proof is needed for the fact that does not admit an equivalent regular expression of lower star height.