Sentence examples for contains the proof from inspiring English sources

The Appendix contains the proof.

The last section contains the proof of the main result.

Section 3 contains the proof of our main result.

This appendix contains the proof of the concavity of ( varPi_{text{S}} ) and ( varPi_{text{M}} ).

The proof for even d is given in Appendix F, while Appendix G contains the proof for odd d.

Section 3 contains the proof of the existence of one solution of (1.1) when the nonlinearity f and (h_{0}), (h_{N}) satisfy some suitable sign conditions.

Section 4 contains the proofs of results presented.

Section 3 contains the proofs of the main theorems.

The Section 3 contains the proofs of these results.

Section 4 contains the proofs of Theorems 1.1-1.3 1.1-1.3

Section 4 contains the proofs of the important inequalities used in Section 3.