reserve z,z1,z2 for Complex;
reserve r,x1,x2 for Real;
reserve p0,p,p1,p2,p3,q for Point of TOP-REAL 2;

theorem Th39:
  for x,y being Element of COMPLEX holds Re (x .|. y) = (Re x)*(Re
  y)+(Im x)*(Im y)
proof
  let x,y be Element of COMPLEX;
  x .|. y =(Re x)*(Re y)+(Im x)*(Im y)+(-((Re x)*(Im y))+(Im x)*(Re y))*
  <i> by COMPLEX2:29;
  hence thesis by COMPLEX1:12;
end;
