Sentence examples for both lemmas are valid from inspiring English sources

Here, following [6], we show that both lemmas are valid for the case of our general function (beta(t)).

As (varepsilon_{1}> frac{pi}{2}) and (varepsilon _{2}> frac{pi}{2}), the results of these lemmas are valid, in particular, in the entire interval (( 0, frac{pi}{2} )).

Both associative and Lie CD-lemmas are valid when we replace the base field k by an arbitrary commutative ring K with identity because we assume that all GS bases consist of monic polynomials.

The following lemma is valid.

Thus, the following lemma is valid.

It is clear that the following lemma is valid.

Then, by (3.3), it follows that the lemma is valid.

Suppose that the lemma is valid up to n.

Therefore the conclusion of the lemma is valid in this case.

If (c_{2}=0), then the statement of the lemma is valid for (i=2).

Assume now the lemma is valid for some integer (kge2), and suppose then E_{0}(x in H^{2malpha}(Omega),quadquad n_{0}(x in H^{mbeta}(Omega),quadquad phi _{0}(x in H^{2+ m-1 beta}(Omega),quad m=k+1.