 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem Th60:
  for D being set holds
    the_unity_wrt the multF of D*+^ = {}
proof
  let D be set;
  set N = D*+^, f = op(N);
  carr(N) = D* & {} = <*>D by Def34;
  then reconsider a = {} as Element of N by FINSEQ_1:def 11;
  now
    let b be Element of N;
    thus f.(a,b) = a[*]b .= {}^b by Def34
      .= b by FINSEQ_1:34;
    thus f.(b,a) = b[*]a .= b^{} by Def34
      .= b by FINSEQ_1:34;
  end;
  then a is_a_unity_wrt op(N) by BINOP_1:3;
  hence thesis by BINOP_1:def 8;
end;
