reserve S for Subset of TOP-REAL 2,
  C,C1,C2 for non empty compact Subset of TOP-REAL 2,
  p,q for Point of TOP-REAL 2;
reserve i,j,k for Nat,
  t,r1,r2,s1,s2 for Real;
reserve D1 for non vertical non empty compact Subset of TOP-REAL 2,
  D2 for non horizontal non empty compact Subset of TOP-REAL 2,
  D for non vertical non horizontal non empty compact Subset of TOP-REAL 2;
reserve s for rectangular FinSequence of TOP-REAL 2;

theorem Th88:
  for f being rectangular FinSequence of TOP-REAL 2 holds LeftComp
  f misses RightComp f
proof
  let f be rectangular FinSequence of TOP-REAL 2;
A1: LeftComp f is_a_component_of (L~f)` by GOBOARD9:def 1;
A2: RightComp f is_a_component_of (L~f)` by GOBOARD9:def 2;
A3: (L~f)`=LeftComp f \/ RightComp f by GOBRD12:10;
  consider A1,A2 being Subset of TOP-REAL 2 such that
A4: (L~f)` = A1 \/ A2 and
A5: A1 misses A2 and
  (Cl A1) \ A1 = (Cl A2) \ A2 and
A6: A1 is_a_component_of (L~f)` and
A7: A2 is_a_component_of (L~f)` by Def3;
  (L~f)`<> {} by Def3;
  then { LeftComp f, RightComp f } = { A1,A2 } by A4,A6,A7,A1,A2,A3,Th7;
  then LeftComp f = A1 & RightComp f = A2 or LeftComp f = A2 & RightComp f =
  A1 by ZFMISC_1:6;
  hence thesis by A5;
end;
