reserve GX,GY for non empty TopSpace,
  x,y for Point of GX,
  r,s for Real;
reserve Q,P1,P2 for Subset of TOP-REAL 2;
reserve P for Subset of TOP-REAL 2;
reserve w1,w2 for Point of TOP-REAL 2;
reserve pa,pb for Point of TOP-REAL 2,
  s1,t1,s2,t2,s,t,s3,t3,s4,t4,s5,t5,s6,t6, l,sa,sd,ta,td for Real;
reserve s1a,t1a,s2a,t2a,s3a,t3a,sb,tb,sc,tc for Real;

theorem Th29:
  for s1,t1,s2,t2,P,Q st
  P = {p where p is Point of TOP-REAL 2:s1<p`1 & p`1<s2 & t1<p`2 & p`2<t2} &
  Q = {qc where qc is Point of TOP-REAL 2:
  not (s1<=qc`1 & qc`1<=s2 & t1<=qc`2 & qc`2<=t2)} holds P misses Q
proof
  let s1,t1,s2,t2,P,Q;
  assume that
A1: P= {p where p is Point of TOP-REAL 2:s1<p`1 & p`1<s2 & t1<p`2 & p`2<t2} and
A2: Q= {qc where qc is Point of TOP-REAL 2:
  not (s1<=qc`1 & qc`1<=s2 & t1<=qc`2 & qc`2<=t2)};
A3: P={|[sa,ta]|:s1<sa & sa<s2 & t1<ta & ta<t2} by A1,Th21;
  Q= {|[sb,tb]| : not (s1<=sb & sb<=s2 & t1<=tb & tb<=t2)} by A2,Th22;
  hence thesis by A3,Th20;
end;
