Sentence examples for and so the assertion from inspiring English sources

and so the assertion holds.

Thus, (operatorname{Fix}(T ) = {z}) and so the assertion (a) holds true.

Hence, if (|u|_{H_{0}^{s}(Omega)}to+infty), then (I u to-infty ), sI u to-infty by asincetion, and so the assertion of Lemu> 4.7 follows.

By the same reasoning as above, one has that | M / M ′ | is an even number, a contradiction; and so the assertion holds.

(3.9) According to (3.8) and (3.9), we have int_{epsilon}^{r}frac {mathrm{d}x}{g(x)}leq b biggl{ 1+ frac {h (r+Lambda^{g (r+Lambda^ biggr}, which is a contradiction to (3.2), and so the assertion is proved.

Then { x r } r > 0 is an -EFE for the pair ( f, g ) with respect to K and so the first assertion of the theorem is proved.

A discrete Helmholtz decomposition in  [30] leads to discrete reliability and so restricts the assertion to simply connected domains Ω for d = 2.  □ Stability (A1) and reduction (A2), Efficiency  (4.6) plus the discrete reliability (A4) and the quasi-orthogonality follow as in Section  5.2.

A discrete Helmholtz decomposition in  [30] leads to discrete reliability and so restricts the assertion to simply connected domains Ω for d = 2.  □ Consequence 6.8 The adaptive algorithm leads to robust convergence with quasi-optimal rate in the sense of   Theorems  4.1 and 4.5.

So the assertion that stress underlies 99percentt of illness may indicate more about the healthy than the sick.

So, the assertion follows from Theorem 2.6.

So the assertion follows from Proposition 1.3 in [23].