 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 Th37:
  for M being well-unital uniquely-decomposable non empty
  multLoopStr for N being non empty MonoidalSubStr of M holds
    N is uniquely-decomposable
proof
  let M be well-unital uniquely-decomposable non empty multLoopStr;
  let N be non empty MonoidalSubStr of M;
A1: un(M) = un(N) by Def25;
  N is SubStr of M & un(M) = the_unity_wrt op(M) by Th17,Th21;
  hence thesis by A1,Th36;
end;
