@Carl Love thank you again for expanding upon this for me. I'll be sure to keep this in mind moving forward.
I'm still trying to understand why ∀x in ℂ the inequality would be false. That is essentially saying something like 1+i != 1+i when it clearly is.
I'm ok with having to provide the assumption, and thanks to you I now know that I need to do so, but I suppose I don't understand why the assumption is needed in the special case where LHS=RHS unambiguously and without any qualifications necessary on the space it is in.
The fact that the software is programmed in this fashion makes me feel like I'm missing an extremely fundamental mathematics concept here about inequalities. Especially since this software has a lot of "student" items and this seems like unneccessary extra requirments for a beginning user.. lets say a student in Calculus 2 comparing sequences for convergence.
can you, or anyone provide an analytical contradiction to x <= x not being true for any space? Specifically, Complex since you mentioned that is the default assumption when using algebraic operands.
Again, i'm okay with having to provide the assumptions i'm just curious why it is needed in the case of this inequality? if it is required by the software to function properly then I would think that it should be returned as an error or at the very least a warning message.
thanks for all of your feedback, I greatly appreciate it.
 additionaly this screenshot underscores what I am trying to understand. If the <= is False but the = is True I don't understand why the software is saying one is False and the other is True because as you mentioned early the logical or operator means one or the other, but not necessarily both.