Sentence examples for is thus complete from inspiring English sources

end{aligned} The proof is thus complete.

The proof is thus complete by taking z ˜ = z ε. □.

The proof of the lemma is thus complete.

The proof of inequality (2.4) is thus complete.

The proof of the first half of Theorem 3.4 is thus complete.

Therefore, S must be upper semi-continuous on M. The proof is thus complete.

The proof is thus completed.

Our proof Theorem 2 is thus completed.

The proof of Lemma 4.1 is thus completed.

The proof of Proposition 3.1 is thus completed.

The proof of Corollary 2.13 is thus completed.