How to assert that a list of variables is real in a nice and clean way

Question

You can use the function Element to say e.g. $x,y,z\in\mathbb{R}$ via Element[x | y | z, Reals].

Now if I have a list of elements and want to say that they are all real I could do:

list = Array[x @ # &, 8]
Element[#, Reals]& /@ list /. List -> And

However, that seems unnecessarily complicated. Is there an easier way? Easier meaning shorter but also clear and easy to understand.

Answer 1

The most straight-forward adaptation of your code is the following:

list = Array[x, 8];
Apply[And, Element[#, Reals]& /@ list
(* x[1] ∈ Reals && x[2] ∈ Reals && x[3] ∈ Reals && x[4] ∈ Reals && x[5] ∈ Reals && x[6] ∈ Reals && x[7] ∈ Reals && x[8] ∈ Reals *)

Also, you can do

Element[Alternatives @@ list, Reals]

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You can also do (according to GuessWhoItIs),

list ∈ Reals

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Often, lists of assumptions are fine, so you can use (according to Bichoy)

Element[#, Reals] & /@ list