Sentence examples similar to proofs were available from inspiring English sources

(all proofs are available in the Supplementary Material).

N k(S) denotes all vertices at distance k (k edges) or less from all vertices of S. To improve the efficiency of the algorithm we use some theoretical results and properties (the detailed proofs are available in Supplement 1).

More worrying proof was available.

A Strange Coexistence The proof is available at crossing points like Chamchamal, on the desert floor about 40 miles outside Sulaimaniya.

Bamber's lawyers have recently obtained a copy of a note from the Home Office database endorsing that tests were needed to ascertain how hot the silencer became after firing, but again no proof is available that this was pursued.

When Zall announced his discovery, or theory, of Coleridge's authorship of the 1821 translation, he was congratulated by fellow scholars but told that his case "would be better made if made more reticently", and it was suggested that he should wait until a more thorough stylistic proof was available.

The detailed proof is available in [8].

The corresponding proof is available in Appendix 1.

Sufficient proof is available today to demonstrate that dental pulp tissue engineering is possible.

That's scary (and more proof is available if you click the link below).

Proof of Lemma 2. The proof is available in the Appendix.