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

theorem
  Re (a*<i>) = 0
proof
  thus Re (a*<i>) = Re a * Re (<i>) - Im a * Im (<i>) by Th9
  .= Re a * 0 - 0 * Im (<i>) by Th7
  .= 0;
end;
