I've sometimes seen that this operator is used to specify that each of given variables is in some set, e.g.
(x|y|z) ∈ Reals as a shorthand for
x ∈ Reals && y ∈ Reals && z ∈ Reals. This was in the context of specifying
Assumptions to functions like
But I remember that when I tried something like this (don't remember exactly what), for some reason it gave me unexpected results, so I've been staying clear of this syntax for a while.
I've read the the documentation on the
is a pattern object that represents any of the patterns $p_i$.
If a named pattern such as
x_appears in $p_i$ that are not used in a particular match, then the named pattern is taken to have a value that is a zero-length sequence
But that didn't make it clear what the "any" means.
Now I'm wondering: what is the difference between the two variants?
FullSimplify for equality doesn't appear to say
True, so I assume they are different. What are the conditions for
(x|y|z)∈Reals to mean exactly that each of $x$, $y$ and $z$ is in $\mathbb R$, as does the