reserve x,y for set,
  n,m for Nat,
  r,s for Real;
reserve f, g for Function;

theorem
  for t being FinSequence of INT ex u being FinSequence of REAL
  st t,u are_fiberwise_equipotent & u is FinSequence of INT
  & u is non-increasing
proof
  let t be FinSequence of INT;
  consider u be non-increasing FinSequence of REAL such that
A1: t,u are_fiberwise_equipotent by Th22;
  take u;
  thus t,u are_fiberwise_equipotent by A1;
  rng t = rng u by A1,CLASSES1:75;
  hence u is FinSequence of INT by FINSEQ_1:def 4;
  thus thesis;
end;
