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"the reverse implication" is correct and can be used in written English.
It can be used to indicate that a logical conclusion can be drawn by reversing a previously stated statement. For example, "It is important to remember that if you are telling the truth, then the reverse implication is that you should not lie."
Exact(21)
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.
Similar(39)
However, the reverse implications are not true.
Furthermore, the reverse implications are valid.
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).
Corollary 2.8 Suppose that A = ( F ˜, A ) and B = ( G ˜, B ) are two IVF soft sets over U. Then we have A ≡ B ⇒ A = L B ⇒ A = J B. It is worth noting that all the reverse implications in Proposition 2.7 and Corollary 2.8 do not hold in general.
In it we use \ \Leftarrow\) for reverse implication.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com