theorem Th17:
  p in LeftComp f iff not p in L~f & not p in RightComp f
proof
  LeftComp f misses RightComp f by Th14;
  then
A1: (L~f)` = LeftComp f \/ RightComp f & LeftComp f /\ RightComp f = {} by
GOBRD12:10;
  p in L~f iff not p in (L~f)` by XBOOLE_0:def 5;
  hence thesis by A1,XBOOLE_0:def 3,def 4;
end;
