reserve a,b,k,m,n,s for Nat;
reserve c,c1,c2,c3 for Complex;
reserve i,j,z for Integer;
reserve p for Prime;
reserve x for object;
reserve f,g for complex-valued FinSequence;

theorem Th67:
  <*1,1*> is a_solution_of_Sierp168
  proof
    set f = <*1,1*>;
    set h = f|1;
    set g = h" ^2;
    g = <*1*>
    proof
      dom g = dom(h") /\ dom(h") by VALUED_1:def 4;
      then
A1:   len g = len h by VALUED_1:def 7,FINSEQ_3:29;
      hence len g = len <*1*>;
      let k;
      assume 1 <= k <= len g;
      then
A2:   k = 1 by A1,XXREAL_0:1;
      h".1 = (h.1)";
      hence <*1*>.k = (h".1)^2 by A2
      .= g.k by A2,VALUED_1:11;
    end;
    hence thesis;
  end;
