Sentence examples for apply to prove from inspiring English sources

(The "real world" in this case being that which came before the birth of our reality-universe and "this remarkable theoretical edifice" being all of the mathematical arguments that we presently apply to prove we know what came before the Big Bang).

Proof: Mathematical induction is applied to prove the claim.

The mathematical induction is applied to prove this lemma.

The mathematical induction is also applied to prove this theorem.

Finally, an exploratory and confirmatory factor analysis was applied to prove its structural soundness and unifactoriality.

Lyapunov stability theorem is applied to prove the stability of the dynamic system.

Local asymptotic normality is established and applied to prove Hájek's convolution theorem for this functional.

This theorem will be applied to prove our main results in the next section.

Now we give a proposition, which will be applied to prove Theorem 1.1.

The same arguments can be applied to prove (i) by taking μ(G ≡0.

By the similar technique that was applied to prove (3.10), we obtain (3.21).