Sentence examples for a proof is given from inspiring English sources

A proof is given in Appendix Appendix B. □.

A proof is given in Appendix Appendix C. □.

A proof is given in Appendix Appendix A. □.

A proof is given to show the good minimum distance property of constructed GF q -LDPC codes.

A proof is given that MEBN can represent a probability distribution on interpretations of any finitely axiomatizable first-order theory.

A proof is given to point out that the government-as-the-provider strategy is the best in terms of social efficiency under some mild assumptions.

For a simplified system model a mathematical proof is given that for a system, designed by Dutch rules of thumb under spatially homogeneous load, local control is nearly as effective as central control when it concerns the prevention of CSO events.

A new proof is given for a result due to N. Grønbæk on characterizing of amenability for Beurling algebras.

The underlined optimization problem P2 is a convex optimization problem, and a detailed proof is given in Appendix 1 Proof the convexity of P2.

A sketch of the proof for Theorem 1 is provided here and a detailed proof is given in the Appendix.

A similar proof is given for S4.