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

theorem Th67:
  for D be non empty set, F be PartFunc of D,REAL, X be set,
      Y being finite set st Y = dom(F|X) holds len FinS(F,X) = card Y
proof
  let D be non empty set, F be PartFunc of D,REAL, X be set;
  let Y be finite set;
  reconsider fs = dom FinS(F,X) as finite set;
A1: dom FinS(F,X) = Seg len FinS(F,X) by FINSEQ_1:def 3;
  assume
A2: Y = dom(F|X);
  FinS(F,X), F|X are_fiberwise_equipotent by A2,Def13;
  hence card Y = card fs by A2,CLASSES1:81
    .= len FinS(F,X) by A1,FINSEQ_1:57;
end;
