reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;

theorem Th68:
  for n be Nat holds iter(R,n+1) = R*iter(R,n)
proof
  let n be Nat;
  consider p being sequence of  bool [:field R,field R:] such
  that
A1: p.(n+1) = iter(R,n+1) & p.0 = id(field R) and
A2: for k being Nat holds p.(k+1) = R*p.k by Def10;
  p.(n+1) = R*p.n by A2;
  hence thesis by A1,A2,Def10;
end;
