 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 Th63:
  for F being non empty SubStr of D*+^ for p,q being Element of F
  holds p[*]q = p^q
proof
  let F be non empty SubStr of D*+^, p,q be Element of F;
  carr(F) c= carr(D*+^) by Th23;
  then reconsider p9 = p, q9 = q as Element of D*+^;
  thus p[*]q = p9[*]q9 by Th25
    .= p^q by Def34;
end;
