Sentence examples for for a proof and from inspiring English sources

Implications for a proof and proving landscape for school mathematics are discussed.

For a proof and other details, see, for example, [16].

Note that P i ((T i u) ⊙ (T i u)) = P i T i (u ⊙ u) (see Appendix 2 for a proof), and thus we can state P i T i ψ a -Pi ((Tiu) ⊙ (T i u)) = P i T i ϕ ).

Much stronger dynamical and probabilistic conditions seem to be needed for such a proof, and even then it remains a difficult problem whether these are satisfied in a realistic gas model.

She answered an advertisement for a proof reader and editor at Puzzler where her linguistic skills were swiftly noticed and she was offered a full-time position.

end{aligned} Here is another lemma (see [3] for a detailed proof and for more details on fractional calculus).

For a detailed proof and more examples, see [[24], Examples 1-5].

For a proof, see e.g., Rescher and Urquhart 1971 and Goldblatt 1987.

For a proof, see Hella, Väänänen, and Westerståhl (1997).

For a proof not using ordinals, and so formulable in Zermelo set theory, see Bourbaki 1950 or Lawvere and Rosebrugh 2003 (Appendix B). 10.

The reader is referred to (Barron et al. 2003) for a proof of the existence and uniqueness of the conditional essential supremum/infimum.