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 Th24:
  (0.X).|.x = 0
proof
  09(X) .|. x = (x + (-x)) .|. x by RLVECT_1:5
    .= x .|. x + (-x) .|. x by Def11
    .= x .|. x + ( - x .|. x ) by Th18;
  hence thesis;
end;
