\title{Given produit}
\author{Gang Xiao}
\email{xiao@unice.fr}
\language{en}
\options{nofloat}
\methods{ineq/addterm, ineq/mulexp, ineq/divexp, ineq/exsides,
ineq/trans, ineq/addineq, ineq/mulineq,
prf/contrapose}
\minsteps{3}

\matrix{vars=a,b
c,d
x,y
r,s
s,t
p,q
}
\text{vars=randomrow(\vars)}
\text{x=item(1,\vars)}
\text{y=item(2,\vars)}

\integer{a=random(3..20)}
\integer{b=random(3..20)}
\integer{prod=\a*\b}
\text{empty=}

\text{eqr=random(,=)}
\text{less=<\eqr}
\text{more=>\eqr}
\text{ctx1=\x*\y \less \prod}
\text{ctx2=\x \more \a}
\text{prv=\y \less \b}

\context{\ctx1
\ctx2}
\goal{\prv}
\text{oldgoal=\goal}

\statement{Let \(\x) and \(\y) be two real numbers with \(\ctx1) and \(\ctx2).
Prove	\( \oldgoal ).
}

