theorem Th24:
  V is Submodule of V
proof
A1: the rmult of V = (the rmult of V) |([:the carrier of V, the carrier of R
  :] qua set) by RELSET_1:19;
  0.V = 0.V & the addF of V = (the addF of V) | ([:the carrier of V, the
  carrier of V :] qua set) by RELSET_1:19;
  hence thesis by A1,Def2;
end;
