theorem Th22:
  Carrier (r(*)LR) c= r*Carrier LR
  proof
    let x be object such that
    A1: x in Carrier(r(*)LR);
    reconsider v=x as Element of R by A1;
    A2: (r(*)LR).v<>0 by A1,RLVECT_2:19;
    (0 qua Real)(*)LR=ZeroLC(R) by Def2;
    then A3: r<>0 by A1,RLVECT_2:def 5;
    then (r(*)LR).v=LR.(r"*v) by Def2;
    then A4: r"*v in Carrier LR by A2;
    r*(r"*v) = (r*r")*v by RLVECT_1:def 7
            .= 1*v by A3,XCMPLX_0:def 7
            .= v by RLVECT_1:def 8;
    hence thesis by A4;
  end;
