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  Th38:
  b "**" <%d1,d2%> = b.(d1,d2)
proof
  len <%d1,d2%>=2 by AFINSQ_1:38;
  then consider f be sequence of D such that
A1: f.0 = <%d1,d2%>.0 and
A2: for n st n+1 < 2 holds f.(n + 1) = b.(f.n,<%d1,d2%>.(n + 1)) and
A3: b "**" <%d1,d2%> = f.(2-1) by Def8;
  f.(zz+1)=b.(f.zz,<%d1,d2%>.(zz+1)) by A2;
  hence thesis by A1,A3;
end;
