Sentence examples for for their proof from inspiring English sources

Because many important theorems in classical mathematics depend for their proof upon the principles affected, large parts of classical mathematics are called into question.

Mr. Diana had by chance seen the name last year when he was challenging the authors for their proof of some alle gations.

Michael Atiyah and Isadore Singer are to share the $875,000 award for their proof of a theorem that links two very different areas of mathematics--topology and differential equations.

In the case of these formulae, the ordinary machinery of truth-functional and quantifier logic suffices for their proof; and Prior showed that the same is true of the two rules of the tense calculus.

For their proof-of-concept research, the team collected data from the notorious 12th hole at Georgia's Augusta National Golf Club, site of the annual Masters Golf Tournament.

Please see [41] for their proofs.

For their proofs, we refer to [23, 24].

We use the following lemmas in the proof of the main result and refer to [1] for their proofs.

We recall the following definitions and lemmas of cone integration and refer to [11, 12] for their proofs.

Indeed, this was the primer pair selected by Hebert and colleagues for their proof-of concept study on Canadian moths, where they propose the DNA barcoding approach for species identification [ 4].

For completeness, we list them and skip their proof for conciseness.