reserve A for non empty set,
  a for Element of A;
reserve A for set;
reserve B,C for Element of Fin DISJOINT_PAIRS A,
  x for Element of [:Fin A, Fin A:],
  a,b,c,d,s,t,s9,t9,t1,t2,s1,s2 for Element of DISJOINT_PAIRS A,
  u,v,w for Element of NormForm A;
reserve K,L for Element of Normal_forms_on A;
reserve f,f9 for (Element of Funcs(DISJOINT_PAIRS A, [:Fin A,Fin A:])),
  g,h for Element of Funcs(DISJOINT_PAIRS A, [A]);

theorem Th11:
  c in -B implies ex g st (for s st s in B holds g.s in s`1 \/ s`2
) & c = [{ g.t1 : g.t1 in t1`2 & t1 in B }, { g.t2 : g.t2 in t2`1 & t2 in B }]
proof
  assume c in -B;
  then
  c in { [{ g.t1 : g.t1 in t1`2 & t1 in B }, { g.t2 : g.t2 in t2`1 & t2 in
  B }] : s in B implies g.s in s`1 \/ s`2 } by XBOOLE_0:def 4;
  then
  ex g st c = [{ g.t1 : g.t1 in t1`2 & t1 in B }, { g.t2 : g.t2 in t2`1 &
  t2 in B }] & for s st s in B holds g.s in s`1 \/ s`2;
  hence thesis;
end;
