Sentence examples for thus finish from inspiring English sources
We thus finish our demonstration.
We thus finish the proof.
We thus finish the proof of Theorem 4.2.
These inequalities lead to (Vert K_{P}yVert leq CVert yVert _{1}), where (C =frac{1}{Gamma (alpha)} ( 1 + Vert T^{dagger} Vert _{mathcal{L(H }} ( 1 + Vert AVert _{mathcal{L(H }} )) ) and thus finish the proof of the lemma.
end{aligned} (31) Combining the two FBSDE-LQ-SOCs (31) for the cases (i=1) and (i=2), we get FBSDE-LQ-NZSSDG (28), and we thus finish the proof.
Combining with (3.22), (3.23), and the weighted Hardy inequality associated with the Greiner-type vector fields (3.2) on the nonisotropic Heisenberg group (3.4), then we only need to do the same steps as in Theorem 2.4 and thus finish the proof of Theorem 3.3.
With Broad departed, Johnson did not return and thus finished the innings wicketless.
Brooke Hamilton, Nancy Patterson, Courtney Collins, Lauren Gim and Liz Washburn thus finished their high school careers without losing.
Danny Care and Mike Brown scored for Quins, who thus finished the regular season at the top of the table.
Topalov thus finished with a convincing 3-1 victory and reaffirmed his status as the current world number one.
The proof is thus finished.
