Sentence examples for the converse proved from inspiring English sources

When we turn to f, again we find that the rules uniquely characterize this connective, since (f Left) provides the premiss for an application of (f′ Right) with Γ consisting of (one occurrence of) f and Δ empty, yielding f ≻ f′, with the converse proved similarly.

Another companion inequality to Jensen's inequality is a converse proved by Dragomir and Goh in [4].

The converse was proved by Erdös [2, 3].

The converse theorem was proved by Erdös [3].

The converse part was proved by the study of Erdös in [2].

Therefore, is a weak minimal vector in the set W. The converse part is proved similarly.

In the following we assume V ( t ) = V ( t, t 0, υ, u ) and we recall the definition of RESP, AESP and the stochastic version of the converse Lyapunov theorem proved by Spiliotis and Tsinias [21] as follows.

The converse can be proved 'elementwise', but it is easier to invoke [80, Proposition 5.2.6(1)], which implies that for a Z -graded ring, primeness is equivalent to graded primeness.

Indeed, because the inclusion (operatorname {Im}P subset ker L) can be proved simply, we need only prove the converse one: (ker L subset operatorname {Im}P).

We first prove the converse by deriving the sum-rate constraints and then prove the achievability by providing the achieved sum rate of the joint coding scheme.

Erdös [2] proved the converse.