\title{Given two products}
\author{Gang Xiao}
\email{xiao@unice.fr}
\language{en}
\options{nofloat}
\methods{ineq/rewrite, ineq/simpdeduc, ineq/mulexp, ineq/divexp,
ineq/trans, ineq/addineq
prf/contrapose}
\minsteps{3}

\matrix{vars=a,b,c,d
x,y,z,t
r,s,t,u
p,q,r,s
}
\text{vars=randomrow(\vars)}
\text{vars=shuffle(\vars)}
\text{a=item(1,\vars)}
\text{b=item(2,\vars)}
\text{c=item(3,\vars)}
\text{d=item(4,\vars)}

\text{eqr=random(,=)}
\text{moreless=shuffle(>,<)}
\text{more=item(1,\moreless)\eqr}
\text{less=item(2,\moreless)\eqr}

\matrix{data=positifs,>,\more,\less
négatifs,<,\less,\more
}
\text{data=randomrow(\data)}
\text{posneg=item(1,\data)}
\text{sign=item(2,\data)}
\text{sign2=item(3,\data)}
\text{sign3=item(4,\data)}
\text{ctx1=simplify(\a*\b \less \c*\d)}
\text{ctx2=\a \sign2 \c}
\text{prv=\b \sign3 \d}

\context{\a \sign 0
\b \sign 0
\c \sign 0
\d \sign 0
\ctx1
\ctx2}
\goal{\prv}
\text{oldgoal=\goal}

\statement{Let \(\a, \b, \c, \d) be four \posneg real numbers with
\(\ctx1) and \(\ctx2).
Prove	\( \oldgoal ).
}

