 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
  for G be non empty multMagma, D be non empty Subset of G st
  for x,y being Element of D holds x*y in D
     ex H being strict non empty SubStr of G st the carrier of H = D
       by Lm5;
