reserve x,y,a,b,c,p,q for Real;
reserve m,n for Element of NAT;

theorem
  a <> 0 & n is odd & delta(a,b,c) >= 0 & Polynom(a,b,c,x|^ n)
  = 0 implies x = n-root((-b+sqrt delta(a,b,c))/(2*a)) or x = n-root((-b-sqrt
  delta(a,b,c))/(2*a))
proof
  assume that
A1: a <>0 and
A2: n is odd and
A3: delta(a,b,c)>=0 & Polynom(a,b,c,x|^ n)=0;
  x|^ n = (-b+sqrt delta(a,b,c))/(2*a) or x|^ n = (-b-sqrt delta(a,b,c))/(
  2*a) by A1,A3,POLYEQ_1:5;
  hence thesis by A2,POWER:4;
end;
