reserve K for Ring,
  V1,W1 for VectSp of K;
reserve F for Field,
  V,W for VectSp of F;
reserve T for linear-transformation of V,W;

theorem Th7:
  for V, W being non empty 1-sorted, T being Function of V,W holds
  dom T = [#]V & rng T c= [#]W
proof
  let V, W be non empty 1-sorted, T be Function of V,W;
  T is Element of Funcs([#]V,[#]W) by FUNCT_2:8;
  hence thesis by FUNCT_2:92;
end;
