reserve n,m for Nat,
  r,r1,r2,s,t for Real,
  x,y for set;

theorem
  for D be non empty set, F be PartFunc of D,REAL, X be set, r be Real,
Z be finite set st Z = dom(F|X) & rng(F|X) = {r} holds FinS(F, X) = card(Z) |->
  r
proof
  let D be non empty set, F be PartFunc of D,REAL, X be set, r be Real;
  let dx be finite set such that
A1: dx = dom(F|X);
  set fx = FinS(F,X);
  assume
A2: rng(F|X) = {r};
  F|X, fx are_fiberwise_equipotent by A1,Def13;
  then
A3: rng fx = {r} by A2,CLASSES1:75;
A4: dom fx = Seg len fx by FINSEQ_1:def 3;
  len fx = card dx by A1,Th67;
  hence thesis by A3,A4,FUNCOP_1:9;
end;
