Sentence examples for and this completes from inspiring English sources

And this completes the proof.

Thus,, and this completes the proof.

Then (1) is satisfied and this completes the proof.

Consequently we must have (4.13), and this completes the proof.

Thus, the eigenvalues of are and This completes the proof.

and this completes the proof of the lemma.

So, (4.1) is satisfied and this completes the proof.

and this completes the proof of Theorem 3.3.

Therefore Φ ( z ) ≺ h ( z ) and this completes the proof.

And this completes the proof of the theorem.

which is a contradiction, and this completes the proof.