reserve x,y,y1,y2 for set,
  D for non empty set,
  d,d1,d2,d3 for Element of D,
  F,G,H,H1,H2 for FinSequence of D,
  f,f1,f2 for sequence of D,
  g for BinOp of D,
  k,n,i,l for Nat,
  P for Permutation of dom F;

theorem
  g is commutative implies g "**" <* d1,d2 *> = g "**" <* d2,d1 *>
proof
  assume
A1: g is commutative;
  thus g "**" <* d1,d2 *> = g.(d1,d2) by Th12
    .= g.(d2,d1) by A1,BINOP_1:def 2
    .= g "**" <* d2,d1 *> by Th12;
end;
