Sentence examples for reverse implication from inspiring English sources

The reverse implication is obvious.

Similarly, the reverse implication follows.

The reverse implication is an open problem.

The reverse implication follows from the above lemma.

For the reverse implication, we use the same technique.

The reverse implication does not hold, in general.

Reverse implications do not hold.

However, the reverse implications are not true.

Furthermore, the reverse implications are valid.

Evidently, in an ordered metric space, commutativity ⇒ weak commutativity ⇒ compatibility ⇒ O-compatibility ⇒ weak compatibility but reverse implications are not true in general as substantiated by the following examples.

Petrusel recently pointed out in his interesting paper that any Hardy-Rogers type operator is a Ćirić type operator, but the reverse implications do not hold (see [11] for details).