Sentence examples for above propositions from inspiring English sources

With the above propositions, the suitable transmitter can be found.

Summarizing the above propositions, we obtain the following theorem.

Theorem 1.1 now follows from the above propositions using the triangle inequality.

In order to prove the above propositions, we need the following lemmas.

To prove the above propositions, let us start from the first property.

As seen by the above propositions, it can be positive or negative, depending upon the relative magnitudes of the coefficients.

Since the proof of the above proposition is very similar to that of Proposition 6, we present just an outline of it.

It is also very useful to prove the above proposition.

What does the above proposition mean?

The above proposition is a try in this direction.

Therefore a signature can be forged from the above proposition.