Sentence examples for the proof shows from inspiring English sources

Thus, the proof shows that if ZF is consistent, then so is ZF together with the AC and the CH.

The proof shows that if Φ is only completely row bounded, then Φ is in fact completely bounded.

The proof shows that the 'ugly' inequality (3.5) is stronger than (3.6).

A careful reading of the proof shows that hypothesis (P3) in Theorem 3.1 can be easily replaced by the weaker hypothesis (iii) in Theorem B. Remark 3.3.

Also the proof shows that two relaxation processes are involved in this effect: dissipation by the diffusion term and dissipation by the firing term.

Inspection of the proof shows that if A is generated according to a Gaussian distribution, then the conditions of Theorem 3 will be met with high probability.

One thing the proof showed is that it is a truth of pure logic that those axioms imply Fermat's Last Theorem.

Furthermore, minor modifications to the proof show that the problem remains NP-hard for various restrictions of the topology of the graphs.

The proof showed that R0 was equivalent to the maximum drug effect parameter in the earlier application when the maximum inhibitory or stimulation effect Emax = 1.

The same argument of the above proof shows that the following is a consequence of Theorem 2.2 in [6].

The last proof shows that the coordinate of the interpolated points is independent of the particular focal length chosen, and therefore, the internal camera parameters are not needed.