theorem
  Rea(z + z*') = 2*Rea z & Im1(z + z*') = 0 &
  Im2(z + z*') = 0 & Im3(z + z*') = 0
proof
A1: z = [*Rea z, Im1 z, Im2 z, Im3 z*] by Th17;
  z*' = [*Rea z, -Im1 z, -Im2 z, -Im3 z*] by Th36;
  then z + z*' = [*Rea z+Rea z, Im1 z+ -Im1 z, Im2 z+ -Im2 z, Im3 z+ -Im3 z*]
  by A1,Def6
    .=[*2*Rea z,0,0,0*];
  hence thesis by Th16;
end;
