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 Th13:
  x.|.(a*y) = (a*') * x.|.y
proof
  thus x.|.(a*y) = ((a*y).|.x)*' by Def11
    .= (a*(y.|.x))*' by Def11
    .= (a*') * (y.|.x)*' by COMPLEX1:35
    .= (a*') * (x.|.y) by Def11;
end;
