Sentence examples for complementary proof for from inspiring English sources

In what follows, we shall give a complementary proof for the main result in [1] by giving a proof of (2.4).

In this paper, we give a complementary proof on the paper 'Existence and uniqueness of anti-periodic solutions for prescribed mean curvature Rayleigh equations'.

To do it, Li and Wang in [16] gave a complementary proof.

In this paper, we shall give a complementary proof to correct the errors.

I don't have proof for now".

Theoretic proof for the convergence is given.

This decimal yields a quick proof for.

Barrel Proof for late night.

We omit the proof for brevity.

The proof for and is similar.

The proof for term II is symmetric.