# How to test consistency of two assertions without hacking

Suppose I have a set of assumptions assum = x ∈ Reals && y ∈ Reals and I want to test an assertion like

ineq = (-(x^2*y) + x^2*Sqrt[y*(-x^2 + y)])/(-(x^2*y) + Sqrt[-(x^2*y*(-x^2 + y))]) > 1


How do I do this functionally?

FullSimplify[assum && ineq];

Refine[assum && ineq];

Assuming[assum, AssumptionsAImpossibleIneqQ[ineq]];


All fail to give the correct answer (first two should give False, last one True). What to do???

The only hack I can think of, which is not functional, and which I wish to avoid is:

$Assumptions = assum && ineq;  and look for a $Assumptoins::cas error. But I want to avoid this. What is the function Mathematica is using to resolve a set of assumptions???

• Reduce[ineq, {x, y}] gives False even without the assumptions... Am I missing something? – Marius Ladegård Meyer Aug 5 '18 at 21:58
• @MariusLadegårdMeyer I definitely missed that thanks! Please answer it so I can accept. Please also point out that if I want to include additional assumptions, they have to be appended with And. – QuantumDot Aug 5 '18 at 22:23
• I'd rather you self-answer the post :) That way you know what to include, and maybe you have a nice example showing how it works as well. – Marius Ladegård Meyer Aug 5 '18 at 22:25