theorem Th18:
  c in B =>> C implies ex f st f.:B c= C & c = FinPairUnion(B,
  pair_diff A.:(f,incl DISJOINT_PAIRS A))
proof
  assume c in B =>> C;
  then
  c in { FinPairUnion(B,pair_diff A.:(f,incl DISJOINT_PAIRS A)) : f.:B c=
  C } by XBOOLE_0:def 4;
  then
  ex f st c = FinPairUnion(B,pair_diff A.:(f,incl DISJOINT_PAIRS A)) & f.:
  B c= C;
  hence thesis;
end;
