Re: question on example dealing with exists

• To: mathgroup at smc.vnet.net
• Subject: [mg117442] Re: question on example dealing with exists
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 18 Mar 2011 06:03:03 -0500 (EST)

```On 17 Mar 2011, at 12:32, olfa wrote:

> Hi mathematica community,
>
> here is my input:
> Reduce[kP>= cN &&
>  Exists[{iPP, kPP}, (kPP < cN) && (iP == 1 + iPP &&
>      kP == 3 + 6*iPP + kPP)], {iP, kP}, Reals,
> Backsubstitution -> True]
>
> and here is the output:
> iP > 1/2 && cN <= kP < -3 + cN + 6 iP
>
> it is clear for me how the output for kP was generated but can someone
> help me to find how the output for iP was generated?
>
> thank you very much

Do you mean: how to show (by hand) that iP>1/2 ?
Well,
6 iPP+kPP+3>cN  and kPP<cN
hence
cN<6 iPP+cN+3
that is
0 < 6 iPP + 3
i.e
-1/2 < iPP
but iP==1+iPP hence iP>1/2.

Andrzej Kozlowski

```

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