Sentence examples for explained in the proof from inspiring English sources

end{aligned}On one hand, as explained in the proof of Theorem 2.2, we note that (Lule 0) at point ((x^0,t^0)).

This in turn implies the claimed tightness of (big { |f t, cdot )|^p ;big | ; t in [0,T] big } subset L^1({{mathbb R}^{N}})) as explained in the proof of Proposition 32.

Conversely, if S is a maximal split torus of G then the maximal split torus corresponding to m ( S ) is the maximal split torus of the radical of the reductive group Z G ( R m ( S ) ) = Z G ( s ) = Z G ( S ) as explained in the proof of (1).

We conducted two experimental tests for the proof-of-concept of the rigid body estimation explained in the previous section.

The method of our proof is the same as Tanahashi's argument, whose outline is explained in the previous section.

"In his lectures he would always make a beautiful presentation, which clearly identified all of the assumptions and explained the proof in detail – and then ended precisely when it was supposed to.

We detail this proof in Appendix Appendix 4: proof of proposition 4. We remark that the inequality (0explained in Appendix Appendix 4: proof of proposition 4; therefore, (13) does not imply any additional condition on the system parameters.

The script strains slightly to explain why the proof's authorship can't be verified.

The proofs will be explained in Section 8.

Also we give a comment explaining what the mistake in the proof is, and suggesting what conditions might be appropriate in generalizing fixed point results to cone spaces, where the cone is taken from the infinite dimensional space.

Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail.