Sentence examples for 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.

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

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

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

The definition of (G cdot,cdot )) then implies the last statement of the theorem.

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

This implies the second statement.

The condition f ≠ α implies the last statement of the lemma.

The proof process of [4], Theorem 2 implies the following statements.