What are the pros and cons of using "=>" rather than "->"?

In an ideal world we might be able to use the correct "rightwards arrow from bar" character (u+21A6), but I'm not suggesting we try to make one out of the characters we can type ("|->" looks terrible).

To my mind, "->" is somewhat closer to being mathematically correct, while "=>" reads as "implies", which is probably why lambdas in other languages have confused me.

Is there a lexical justification for choosing "=>" over "->"?

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