Sentence examples for implies the assertion from inspiring English sources

This implies the assertion.

This implies the assertion (2.18).

So, the Δ2-condition implies the assertion.

This relation and the estimate (5.4) implies the assertion.

The sets and have same upper bounds, which implies the assertion.

The negation of existence, therefore, implies the acceptance of nonexistence, while the negation of nonexistence implies the assertion of existence.

Now, we see that (9.4), Proposition 3.4 d) and (9.3) imply the assertions.

Thus (W'(t)leq0), which implies the desired assertion since the equality holds only when ((u,v)= u_,v_)).

When it is positive, (x_{i}(t)), (i=1,ldots,4) tend to infinity which contradicts Theorem 4.1, which implies the required assertion (14).

This implies the lemma's assertion.

Therefore, by using Lemma 3.3, we obtain limsup_{trightarrowinfty}max_{x inOmega}u t, x leq e(r/a+1) (K+epsilon) on Ω̅, which implies the second desired assertion by the continuity as (epsilonrightarrow 0).