theorem
  for A being finite set holds (canFS A)" is Function of A, Seg card A
proof
  let A be finite set;
  len canFS A = card A by Th92;
  then dom canFS A = Seg card A by Def3;
  then
A1: rng ((canFS A)") = Seg card A by FUNCT_1:33;
  rng canFS A = A by FUNCT_2:def 3;
  then dom ((canFS A)") = A by FUNCT_1:33;
  hence thesis by A1,FUNCT_2:1;
end;
