Sentence examples for obviously verify from inspiring English sources

If the sequence { S n } (resp. { T n } ) of averaged mappings consists of a single mapping S (resp. T), then { S n } and { T n } obviously verify conditions (3.1) and (3.2), and hence from Lemma 3.3 we have the following corollary.

Since the expressions of the maximum sum-EST for the suboptimal and optimal schemes are (sum _{n=0}^{K-1}T_{{text {max}}}^{dagger (n)}) and (sum _{n=0}^{K-1}T_{{text {max}}}^{ddagger (n)}), respectively, it obviously verify the maximum sum-EST for the suboptimal or optimal scheme is much larger than that for the round-robin scheme.

Making use of Lemma 2, (w_{3}>0) and the arbitrariness of (bar {varepsilon}_{1}), (limsup_{trightarrowinfty}frac{1}{t}int_{0}^{t}z(s),dsleqfrac {w_{3}k_{2}}{c_{3}}), a.s. is obviously verified.

Obviously, itself verifies.

I obviously can't verify the above quotes, and I know anecdotal evidence should be taken lightly, but this is just a small selection of the responses I got from one casual query.

We obviously had to verify it was OK with the infection control team.

However, "this is obviously difficult to verify and enforce, and it appears not to be satisfied in practice" (Blanchard and Landier, 2002, p. 230).

It's obviously hard/impossible to verify these numbers for us, so it's worth taking them with a grain of salt.

Further investigations are obviously required to verify this finding, including more thorough sampling of the Daphnia transcriptome and functional data such as in situ hybridizations to support the notion that these genes may have contributed to biological innovations.

Obviously I can't verify the validity of these, but as they back my judgement, I'll take 'em.

Corollary 1 If d ( Fix ( T ), ∂ C ) ≜ inf { ∥ x − y ∥ ∣ x ∈ Fix ( T ), y ∈ ∂ C } > 0, then { x n } generated by (2.1) converges strongly to x † = P Fix ( T ) 0. Proof Obviously, it suffices to verify that if d ( Fix ( T ), ∂ C ) > 0, then ∑ n = 1 ∞ ( 1 − λ n ) = ∞.