reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;
reserve a, b, c, d, e, f for object;

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;
