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 Th25:
  for s1,t1,s2,t2,P st
  P = { p0 where p0 is Point of TOP-REAL 2:s1<p0`1 & p0`1<s2
  & t1<p0`2 & p0`2<t2} holds P is convex
proof
  let s1,t1,s2,t2,P;
  assume P = { p0 where p0 is Point of TOP-REAL 2:s1<p0`1 & p0`1<s2
  & t1<p0`2 & p0`2<t2};
  then P={|[sa,ta]|:s1<sa & sa<s2 & t1<ta & ta<t2} by Th21;
  hence thesis by Th8;
end;
