\title{Sum and product of 3 I}
\author{Gang Xiao}
\email{xiao@unice.fr}
\language{en}
\options{nofloat fixedgoal}
\text{methcst=random(constineq,obvineq)}
\text{methtra=random(trans,addineq)}
\methods{ineq/rewrite, ineq/simpdeduc, ineq/mulexp, ineq/lincomb,
ineq/\methcst, ineq/\methtra, ineq/mulineq, ineq/sqrpos}
\minsteps{8}

\matrix{vars=x,y,z
a,b,c
r,s,t
l,m,n
u,v,w
}
\text{vars=randomrow(\vars)}
\text{x=item(1,\vars)}
\text{y=item(2,\vars)}
\text{z=item(3,\vars)}

\integer{n=random(8..30)}
\integer{N=\n^3}
\text{range=random(rational numbers, real numbers)}

\text{less=random(<,<=)}
\text{ctx1=\x + \y + \z \less \n}
\text{ctx2=0 <= \x}
\text{ctx3=0 <= \y}
\text{ctx4=0 <= \z}
\text{prv=\x*\y*\z \less \N}

\context{\ctx1
\ctx2
\ctx3
\ctx4
}
\goal{\prv}

\statement{Let \(\x, \y, \z) be three non-negative \range such that
\( \ctx1 ).
Prove <p><center>
\(\prv).
</center>
}

\if{\newobject != $empty}{
 \text{cut=wims(exec mathexp cut inequality
\newobject)}
 \text{left=item(1,\cut)}
 \text{sign=item(2,\cut)} 
 \text{right=item(3,\cut)}
 \if{\sign issametext \less}{
  \text{test1=simplify(\left-(\x*\y*\z))}
  \text{test2=simplify(\right-(\N))}
 }{
  \text{test1=simplify(\right-(\x*\y*\z))}
  \text{test2=simplify(\left-(\N))}
  \text{sign=wims(translate internal <> to >< in \sign)}
 }
}

\condition{\test1 = 0 and \test2 = 0 and \sign issametext \less}

