reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;
reserve k1,k2 for Nat;
reserve D for non empty set,
  F,G for XFinSequence of D,
  b for BinOp of D,
  d,d1,d2 for Element of D;

theorem  Th39:
  b "**" <%d,d1,d2%> = b.(b.(d,d1),d2)
proof
  set F=<%d,d1,d2%>;
  len F=3 by AFINSQ_1:39;
  then consider f be sequence of D such that
A1: f.0 = F.0 and
A2: for n st n+1 < 3 holds f.(n + 1) = b.(f.n,F.(n + 1)) and
A3: b "**" F = f.(3-1) by Def8;
A4: f.(1+1)=b.(f.1,F.(1+1)) by A2;
  f.(zz+1)=b.(f.zz,F.(zz+1)) by A2;
  hence thesis by A1,A3,A4;
end;
