Sentence examples for proof of the statement from inspiring English sources

The proof of this theorem consists essentially of a formalization in arithmetic of the arithmetized version of the proof of the statement, "If a system is consistent, then p is not provable"; i.e., it consists of a derivation within number theory of p itself from the arithmetic sentence that says that the system is consistent.

This gives the proof of the statement.

(ii) The proof of the statement follows by using Lemmas 4.6-4.9 4.6-4.9d Theorem 2.1.

Thus the proof of the statement (i) of Theorem 3.1 is complete.

end{aligned}This completes the proof of the statement in the example.

Also the proof of the statement (ii) of Theorem 3.1 is complete.

The proof of the statements (i), (ii), (iii) (with ( r k + r ̃ k ) replaced by r k ) can be found in [4].

Both components are intended to serve as proof of the statements of the communicator.

One way to show people that you're not like a high-pressure sales individual is to always provide accessible proof of the statements that you make in your pitch.

The proof of this statement follows the same steps used in the proof of the meridien estimator Property [13] and is thus omitted.

With this construction of the reals, all proofs of the statement 1 =.999... can be viewed as implicitly assuming the equality when any operations are performed on the real numbers.