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 Th7:
  z * (- v) = - (z * v)
proof
  thus z * (- v) = (- (1r * z)) * v by Th6
    .= ((- 1r) * z) * v
    .= (- 1r) * (z * v) by Def4
    .= - (z * v) by Th3;
end;
