Sentence examples for this implies the statement from inspiring English sources

This implies the statement of the lemma.

This implies the statement in the theorem.

Together with the previous claim, this implies the statement.

This implies the statement given for consequence relations (putting "⊩" in place of "⊢") since a generalized consequence relation, like a consequence relation, is always determined by the class of all valuations consistent with it.

This fact implies the statement of Theorem 6 for any positive mean value of ({tilde{s}_{k}}).

This implies the third statement of the lemma and the proof is finished.

This implies the second statement.

(157)Taking for instance ε = 1 / 4, reabsorbing terms and yet adding R - α E 0 to both sides of the resulting inequality, we conclude with Open image in new window (158)This last estimate implies the statement of the theorem, that is M α, R # ( D u ) ( x ) ≤ c S, (159 where c ≡ c ( n, p, ν, L, α ~ ) and S in fact denotes the quantity appearing in the right hand side of (158).

It is easy to see that the statement for (tilde{X}_{t}) implies the statement for (X t)).

By Lemma 3, the determinant of system (11) is different from zero, which implies the statement.

This implies the inequalities in the statement of the lemma.