[PPL-devel] Proof

[Angela Stazzone]

Hi Pat,
can you help me to find a formal proof (or an example it is not true) to
the following assertion?

EXTREMAL RAYS ARE STABLE WHEN COMBINED
 WITH ANY VECTOR OF THE LINEALITY SPACE.

I found it in H. Leverge - A note on Chernikova's Algorithm -
Publication Interne 635 - February 1992 - page 9.

I guess "stable" means that the combination between an extremal ray with
an element of the lin. space is an extremal ray.

I think it is intuitive that it's true, but I can't find a formal proof!

Also, I found (in Leverge page 4) this result:

if the set G = cone{y} + lin.space (C) is
     a face of C, then y is called an extremal ray
     of C and G a minimal proper face of C;

where, given a set X cone{X} is the set of all positive combination of
all vectors in X.

Can this help to demonstrate the assertion above?

Thanks,
   Angela.