reserve x, y, z, s for ExtReal;
reserve i, j for Integer;
reserve n, m for Nat;
reserve x, y, v, u for ExtInt;
reserve
  D for non empty doubleLoopStr,
  A for Subset of D;

theorem
  A |^ 1 = A
  proof
    set f = <*A*>;
A1: len f = 1 & f.1 = A by FINSEQ_1:40;
    now
      let i be Nat such that
A2:   i in dom f & i+1 in dom f;
      dom f = {1} by FINSEQ_1:2,38;
      then i = 1 & i+1 = 1 by A2,TARSKI:def 1;
      hence f.(i+1) = A *' (f/.i);
    end;
    hence thesis by A1,Def4;
  end;
