Sentence examples for proves the validity from inspiring English sources

which proves the validity of (1.4) for.

This proves the validity of the method.

This proves the validity of (16).

It proves the validity of the model.

which proves the validity of (3.13) for all.

This proves the validity of this theorem for case (ii).

Inequality (3.8) proves the validity of inequality (3.3).

It proves the validity of the proposed methods.

This proves the validity of this theorem for case (i).

This proves the validity of our method if calculating the minimum required number of samples.

Note that (2.4) proves the validity of inequality (2.2) for the case (n=1).