Sentence examples for Following proofs from inspiring English sources

These will be useful in the following proofs.

They will be useful in the following proofs.

In this section, we first give the following notations; these will be useful in the following proofs.

For convenience, we give some notation and properties which will be used in the following proofs of our results.

If, all the following proofs are similar.

The following proofs are similar to the one in [45].

People have indeed followed proofs in these systems.

Our proofs of this theorem closely follows proofs given in [11] for some related results.

Proof It follows proof similar to the proof of Lemma 1 of Kiany andAmini-Harandi [22].

Proof Following the proof of Theorem 1, FS ≠ ∅.

Proof Following the proof of Theorem 1, FT ≠ ∅.