reserve i,j for Element of NAT,
  x,y,z for FinSequence of COMPLEX,
  c for Element of COMPLEX,
  R,R1,R2 for Element of i-tuples_on COMPLEX;

theorem Th20:
  for z being Complex holds z+z*' = 2*(Re z)
proof
  let z be Complex;
  z+z*'=Re z + Re (z*')+(Im z + Im (z*'))*<i> by COMPLEX1:81
    .=Re z + Re (z*')+(Im z + -Im z)*<i> by COMPLEX1:27
    .=Re z + Re z by COMPLEX1:27
    .=2*(Re z);
  hence thesis;
end;
