reserve X,Y,z,s for set, L,L1,L2,A,B for List of X, x for Element of X,
  O,O1,O2,O3 for Operation of X, a,b,y for Element of X, n,m for Nat;
reserve F,F1,F2 for filtering Operation of X;
reserve i for Element of NAT;
reserve X for ConstructorDB, A for FinSequence of the Constrs of X,
  x for Element of X;
reserve Y for ref-finite ConstructorDB,
  B for FinSequence of the Constrs of Y,
  y for Element of Y;

theorem Th72:
  for n1,n2,m1,m2 being Nat st n1 <= m1 & n2 <= m2 holds
  EXACTLY+-(B,n1,n2) c= EXACTLY+-(B,m1,m2)
  proof let n1,n2,m1,m2 be Nat;
    assume
A1: n1 <= m1 & n2 <= m2;
    let z be object; assume
A2: z in EXACTLY+-(B,n1,n2); then
    z in {y: card((y ref)\rng B) <= n1 & card((rng B)\y ref) <= n2}
    by Def36; then
    consider y such that
A3: z = y & card((y ref)\rng B) <= n1 & card((rng B)\y ref) <= n2;
    card((y ref)\rng B) <= m1 & card((rng B)\y ref) <= m2
    by A1,A3,XXREAL_0:2; then
    y in {x1 where x1 is Element of Y: card((x1 ref)\rng B) <= m1 &
    card((rng B)\x1 ref) <= m2};
    hence thesis by A2,A3,Def36;
  end;
