FullSimplify with ForAll

• To: mathgroup at smc.vnet.net
• Subject: [mg48624] FullSimplify with ForAll
• From: csr at postmark.net (Sharath)
• Date: Tue, 8 Jun 2004 00:48:15 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Given the input (Mathematica 5.0)

a = (d + 2)/d; b = (1/a)^(1/r^2);
FullSimplify[ForAll[{r, d}, r>=1 && 0 < d && d < 1, 1 - b^(r^2) > 0]]

the output is
\!\(&#8704; \_\({r, d}, r &#8805; 1 && 0 < d && d < 1\)1 -
\((\((d\/\(2 + \
d\))\)\^\(1\/r\^2\))\)\^\(r\^2\) > 0\)

which is the same expression with b expanded, that is,

forall{r,d},r>=1 && 0<d && d<1 1-((d/d+2)^1/(r^2))^(r^2)>0

Why is FullSimplify not cancelling 1/(r^2) and r^2? My interest is a
more complex inequality but FullSimplify is just giving me the
expression back. Then I tested with this simpler inequality and it
still gives me the expression back.

Could anyone know how I should give the input? I want to see if the
expr is Ture or False.

Thanks,

Sharath

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