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

theorem Th12:
  Re(a+b*<i>) = a & Im(a+b*<i>) = b
proof
  reconsider a,b as Element of REAL by XREAL_0:def 1;
  (a+b*<i>) = [*a,b*] by Lm21;
  hence thesis by Lm2;
end;
