reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem
  Re(z + z*') = 2*Re z & Im(z + z*') = 0
proof
  thus Re(z + z*') = Re z + Re (z*') by Th8
    .= Re z + Re z by Th27
    .= 2*Re z;
  thus Im(z + (z*')) = Im z + Im (z*') by Th8
    .= Im z + -Im z by Th27
    .= 0;
end;
