reserve P for Subset of TOP-REAL 2,
  f,f1,f2,g for FinSequence of TOP-REAL 2,
  p,p1,p2,q,q1,q2 for Point of TOP-REAL 2,
  r1,r2,r19,r29 for Real,
  i,j,k,n for Nat;

theorem Th52:
  p1,p2 split P & q in P & q <> p2 implies q,p2 split P
proof
  assume that
A1: p1,p2 split P and
A2: q in P and
A3: q <> p2;
  p2,p1 split P by A1,Th50;
  then p2,q split P by A2,A3,Th51;
  hence thesis by Th50;
end;
