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

\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{more=>}
\text{less=<}
\matrix{data=\x^2 \more \y^2, \x \more= 0, \x \more \y, 2, 4
\x^2 \more \y^2, \x \less= 0, \x \less \y, 3, 3
\x^2 \less \y^2, \y \more= 0, \x \less \y, 2, 4
\x^2 \less \y^2, \y \less= 0, \x \more \y, 3, 3
}
\text{data=randomrow(\data)}
\text{ctx1=item(1,\data)}
\if{random(1,2)=1}{
 \text{ctx2=item(2,\data)}
 \text{prv=item(3,\data)}
 \integer{stp=item(4,\data)}
}{
 \text{ctx2=item(3,\data)}
 \text{prv=item(2,\data)}
 \integer{stp=item(5,\data)}
}
\minsteps{\stp}

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

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

