Sentence examples for terminates the proof from inspiring English sources

Inequality (2.19) terminates the proof of inequality (2.17).

Applying Theorem 4.4 in [7] to the matrix A ̃ w terminates the proof.

Finally, noticing that for ϵ = N -ρ with N ≥ 2, condition (10) always holds when condition (9), with C ρ = 2(3 + ρ C, is satisfied, terminates the proof.

We now proceed by induction, thus completing the proof, for sequence (3.1) terminates.

The tests indicated good fracture stability, and the proof tests carried for each of the two prototypes terminated at more than 350 N due to failure of the loading cable and respectively, secondary mandible fractures occurring away from the miniplate.

The proof.

The proof of everything.

Where's the proof?

Here's the proof.

Proof The proof is by contradiction.

This completes the proof.