reserve FT for non empty RelStr;
reserve x, y, z for Element of FT;
reserve A for Subset of FT;
reserve F for Subset of FT;

theorem
  for FT being filled non empty RelStr, A being Subset of FT holds A^i c= A
proof
  let FT be filled non empty RelStr;
  let A be Subset of FT;
  let x be object;
  assume
A1: x in A^i;
  then reconsider y=x as Element of FT;
A2: y in U_FT y by Def4;
  U_FT y c= A by A1,Th7;
  hence thesis by A2;
end;
