reserve n,m,k for Nat,
  x,y for set,
  r for Real;
reserve C,D for non empty finite set,
  a for FinSequence of bool D;

theorem
  for F be PartFunc of D,REAL, A be RearrangmentGen of C st F is total &
  card C = card D holds Rlor(F,A), Rland(F,A) are_fiberwise_equipotent & FinS(
  Rlor(F,A),C) = FinS(Rland(F,A),C) & Sum (Rlor(F,A),C) = Sum (Rland(F,A),C)
proof
  let F be PartFunc of D,REAL, B be RearrangmentGen of C;
  assume
A1: F is total & card C = card D;
  then
A2: Sum (Rland(F,B),C) = Sum (F,D) & Rlor(F,B), FinS(F,D)
  are_fiberwise_equipotent by Th18,Th23;
  Rland(F,B), FinS(F,D) are_fiberwise_equipotent & FinS(Rland (F,B),C) =
  FinS( F,D) by A1,Th16,Th17;
  hence thesis by A1,A2,Th24,Th25,CLASSES1:76;
end;
