Sentence examples for proof uses from inspiring English sources

The proof uses singular perturbation methods.

This proof uses transfinite induction up to ε0.

This proof uses the cut rule at the topmost step.

The proof uses stochastic integrals and Itô calculus.

The proof uses standard covering lemmas and selection processes.

Proof The proof uses elementary group theory and Theorem 3.1.

The proof uses a faithful embedding of CS4 into positive, negation-free S4.

Notice that this proof uses a principle corresponding to the law of excluded middle.

The proof uses energy methods, which are adaptations of corresponding methods for smooth manifolds.

Among other tools, the proof uses the Rudin Shapiro polynomials and heat kernel estimates.

The proof uses the beautiful Corona argument of Nazarov, Treil and Volberg.