reserve a,b,c,x,y,z for Real;

theorem
  a >= b implies a*sqrt(1+b^2) >= b*sqrt(1+a^2)
proof
  assume
A1: a>=b;
  per cases;
  suppose
    a>=0;
    hence thesis by A1,Lm9;
  end;
  suppose
    a<0;
    hence thesis by A1,Lm7;
  end;
end;
