reserve T for non empty Abelian
  add-associative right_zeroed right_complementable RLSStruct,
  X,Y,Z,B,C,B1,B2 for Subset of T,
  x,y,p for Point of T;
reserve t,s,r1 for Real;
reserve n for Element of NAT;
reserve X,Y,B1,B2 for Subset of TOP-REAL n;
reserve x,y for Point of TOP-REAL n;

theorem Th58:
  1(.)X = X
proof
  thus 1(.)X c= X
  proof
    let x be object;
    assume x in 1(.)X;
    then ex z being Point of TOP-REAL n st x=1*z & z in X;
    hence thesis by RLVECT_1:def 8;
  end;
  let x be object;
  assume
A1: x in X;
  then reconsider x1=x as Point of TOP-REAL n;
  x1=1*x1 by RLVECT_1:def 8;
  hence thesis by A1;
end;
