Sentence examples for proof details from inspiring English sources

Proof: Details are provided in Appendix 1.

Proof: The proof details for this lemma appear in Appendix A.   ■.

Proof: The proof details for Theorem 4 and Corollaries 5 and 6 appear in Appendix D.    ■.

The proof details have been relegated to appendices to keep the subject material simple and clear.

Proof: The proof details for Theorem 1 and its associated Corollaries 2 and 3 appear in Appendix C.   ■.

The proof details in the paper have been relegated to appendices to keep the subject material simple and clear.

Lately Dmitry has been working on a groundbreaking proof detailing how two separate theories, the Hochschild cohomology and the Goldman bracket, can validate the idea of string topology, which uses strings, not points, to study three-dimensional shapes such as bagel-like toroids or pretzels.

Another, T-Rex Global of Fremont, Calif., (www.trexglobal.com), has software that takes you through the process, promising audit-proof detail and even a printout of the completed relevant Form 4562.

In these cases we omit proofs or details of proofs making references to corresponding pages of the articles [3] or [13].

In the cases when we will use the results from other papers we will omit the proofs or details of proofs, but we will refer to them appropriately.

For proof and details, see Guo [22].