theorem
  for x1,y1 being Element of COMPLEX
   for x2,y2 being Real st x1 = x2 &
  y1 = y2 holds addcomplex.(x1,y1) = addreal.(x2,y2)
proof
  let x1,y1 be Element of COMPLEX;
  let x2,y2 be Real;
A1: addcomplex.(x1,y1)= x1+y1 by BINOP_2:def 3;
  assume x1 = x2 & y1 = y2;
  hence thesis by A1,BINOP_2:def 9;
end;
