# Frama-C-discuss mailing list archives

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

```Sorry, my mistake with .2 instead of 2.

The lemma is definitely _correct_ and soundly proved by WP+Z3 in all float models, since the lemma only involves reals.

L.

PS: it is still a mystery for me why Z3 succeed into proving this, but fails into proving (x2 - 2x + 1) >= 0â€¦ :-)

> Le 4 mai 2016 Ã  15:27, cok at frontiernet.net a Ã©crit :
>
> But the original question is about x*x - .2*x + 0.01, not x*x -2*x + 0.01.
>
> With x = 0.5, we get x*x - .2*x + 0.01 == 0.25 - .1 + 0.01 ==.16 > 0
> More to the point
> With x = 0.1, we get x*x - .2*x + 0.01 == 0.01 - .02 + 0.01 == something close to zero, depending...
>
> - David
> From: LoÃ¯c Correnson <loic.correnson at cea.fr>
> To: Frama-C public discussion <frama-c-discuss at lists.gforge.inria.fr>
> Sent: Wednesday, May 4, 2016 8:57 AM
> Subject: Re: [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 <mailto: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/ <http://www.lri.fr/~marche/>
> > F-91405 ORSAY Cedex                    |
>
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