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I am using inequalities to follow some line of reasoning in Mathematica and I came across a problem I can not explain to myself. Does from a>=0 and b>=0 not follow a+b >= 0? How does Mathematica evaluate these statements? Thanks!

In[225]:= Refine[(A0 c0 (c - c1) >= 0), 
  A0 >= 0 && A >= A0 && A1 >= A && c1 >= 0 && c > c1 && c0 >= c]

Out[225]= True

In[226]:= Refine[(A (c0 - c1) c1 >= 0), 
  A0 >= 0 && A >= A0 && A1 >= A && c1 >= 0 && c > c1 && c0 >= c]

Out[226]= True

In[227]:= Refine[(A0 c0 (c - c1) + A (c0 - c1) c1 >= 0), 
  A0 >= 0 && A >= A0 && A1 >= A && c1 >= 0 && c > c1 && c0 >= c]

Out[227]= A0 c0 (c - c1) + A (c0 - c1) c1 >= 0
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    $\begingroup$ Well Refine[a + b >= 0, a >= 0 && b >= 0] returns True, so it is likely the complexity of the final statement that is giving Mathematica trouble. $\endgroup$
    – rcollyer
    Jan 15, 2013 at 15:58

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