Sentence examples for consequently in virtue of from inspiring English sources

Consequently, in virtue of Lemma 1.1 we find that C λ has another fixed point x λ, 2 with x λ, 2 ∈ { K ¯ 2 − K 1, as (H5) holds, K ¯ 2 ′ − K 1, as (H6) holds.

Consequently, in virtue of the weak closeness of (H^{1}_{0}(Omega_{gamma}backslashoverline{omega}_{t^)^{2}times H^{2}_{0}(Omega_{gamma}backslashoverline{omega}_{t^)) we have ((tilde{eta}-{eta})in H^{1}_{0}(Omega_{gamma}backslashoverline{omega}_{t^)^{2}times H^{2}_{0}(Omega_{gamma}backslashoverline{omega}_{t^)).

In virtue of what, precisely, would you distinguish them aesthetically?

In virtue of Eqs.

Then, in virtue of the continuity of, we see that.

or, in virtue of the definition of, (3.11).

In virtue of Lemma 2.5, there exists such that.

In virtue of Lemma 3.1, there exists such that (3.12).

Note that in virtue of Lemma 2.3 and (3.22).

And thus not in virtue of the satisfaction of (ii*).

In virtue of what does the right obtain?