reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;

theorem Th10:
  (z1 - z2) * v = z1 * v - z2 * v
proof
  thus (z1 - z2) * v = (z1 + (- z2)) * v .= z1 * v + (- z2) * v by Def3
    .= z1 * v + z2 * (- v) by Th6
    .= z1 * v - z2 * v by Th7;
end;
