# Frama-C-discuss mailing list archives

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# [Frama-c-discuss] hint assertions and understanding cooperation between wp and value plugin

```With x = 0.5, we get x*x -2*x + 0.01 == 0.25 - 1.0 + 0.01 == -0.74 < 0
There is probably a confusion with (x2 - 2x + 1) = (x-1)2 >= 0, but Z3 is not able to prove itâ€¦
However, Alt-Ergo succeed into proving (x-1)^2 >= 0, and (x^2 - 2*x + 1 == (x-1)^2.
L.

> Le 4 mai 2016 Ã  14:07, Claude MarchÃ© <Claude.Marche at inria.fr> a Ã©crit :
>
>
> Sorry to interfere, but I don't understand the meaning of "wrong in WP"
>
> According to ACSL manual, this lemma is a statement expressed purely in
> mathematical real arithmetic, and as such it is valid. It is indeed
> proved automatically by Z3 4.4.1.
>
> If you want to state a similar property talking about floating-point
> arithmetic, it should be stated differently, typically using a program
>
> void f(double x) {
>  double y = x*x - .2 * x + 0.01;
>  //@ assert y >= 0.0;
> }
>
> But I guess it probably wrong because of rounding, even with a
> precondition like \abs(x) <= 1.0
>
> My two cents,
>
> - Claude
>
> Le 04/05/2016 13:54, LoÃ¯c Correnson a Ã©crit :
>>> /*@ lemma sq_double: \forall real x; x*x - .2 * x + 0.01 >= 0.; */
>>
>> This lemma is definitely wrong in WP with Real model (not float there).
>> At least, it is not provable in the forthcoming release of Frama-C.
>> Is there a bug in some existing release?
>> 	L.
>>
>>
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>>
>
> --
> Claude MarchÃ©                          | tel: +33 1 69 15 66 08
> INRIA Saclay - ÃŽle-de-France           |
> UniversitÃ© Paris-sud, Bat. 650         | http://www.lri.fr/~marche/
> F-91405 ORSAY Cedex                    |
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