 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 a,b being Element of D*+^+<0> holds a [*] b = a^b
proof
  let a,b be Element of D*+^+<0>;
  the multMagma of D*+^+<0> = D*+^ by Def22;
  then reconsider p = a, q = b as Element of D*+^;
  thus a [*] b = p [*] q by Th18
    .= a^b by Def34;
end;
