theorem Th73:
  A c= B implies Lin(A) is Submodule of Lin(B)
proof
  assume
A1: A c= B;
  now
    let v;
    assume v in Lin(A);
    then consider l such that
A2: v = Sum(l) by Th67;
    reconsider l as Linear_Combination of B by A1,Th19;
    Sum(l) = v by A2;
    hence v in Lin(B) by Th67;
  end;
  hence thesis by RMOD_2:28;
end;
