Having a hard time differentiating among the following:
X necessarily implies Y
X necessarily yields Y
X conclusively demonstrates Y
The last example above surely is X --> Y, but I'm not so clear about the first two.
Here are examples of how both have been used in a legal opinion:
A judgment in favor of the plaintiff would "necessarily imply" the invalidity of his conviction or sentence.
Here, success in Skinner's suit for DNA testing would not "necessarily imply" the invalidity of his conviction.
A Brady claim, when successful... "necessarily yields" evidence undermining a conviction.