reserve X for non empty CUNITSTR;
reserve a, b for Complex;
reserve x, y for Point of X;
reserve X for ComplexUnitarySpace;
reserve x, y, z, u, v for Point of X;

theorem Th29:
  |.(x.|.x).| = Re(x.|.x)
proof
A1: Im (x.|.x) = 0 by Def11;
  Re (x.|.x) >= 0 by Def11;
  then |.Re(x.|.x)+Im(x.|.x)*<i>.| = Re (x.|.x) by A1,ABSVALUE:def 1;
  hence thesis by COMPLEX1:13;
end;
