Sentence examples for proof result from inspiring English sources

A result is presented together with its proof (Result 1), and the model of weighted goal programming with logarithmic deviational variables is then presented.

The sections for goal geometric programming model with logarithmic deviational variables and its solution procedure are followed by a theorem on the model of weighted goal programming with logarithmic deviational variables and its proof (Result 2).

A "moderate," "weak," or "very weak" level of proof resulted in a "conditional" recommendation ("should probably be done", "should probably not be done…").

Using similar arguments as in the proof of result (iii), result (iv) can be proved.

These aren't methods that generate fool-proof results, of course, and there's a lot that can't be seen reliably with the naked eye.

In particular, our approach reduces the complexity of the required proofs, resulting in fewer proof obligations that need to be discharged at the target machine.

No matter how clever the proof, the result is to replace the fantastic with the ordinary.

This completes the proof of Result 1.

Proof The result follows from Calciano [11].

Proof The result follows from Lemma 3. □.

This finishes the proof of result (iii).