reserve X, Y for non empty set;
reserve X for non empty set;
reserve R for RMembership_Func of X,X;

theorem Th26:
  for n being Nat holds (n+1) iter R = (n iter R) (#) R
proof
  let n be Nat;
  consider f being sequence of Funcs([:X,X:],[. 0,1 .]) such that
A1: (n+1) iter R = f.(n+1) & f.0 = Imf(X,X) and
A2: for k being Nat ex Q being RMembership_Func of X,X st f.k
  = Q & f.(k + 1) = Q (#) R by Def9;
  ex Q being RMembership_Func of X,X st f.n = Q & f.(n + 1) = Q(#)R by A2;
  hence thesis by A1,A2,Def9;
end;
