
theorem Th9:
  for p1,p2 being Point of TOP-REAL 2, a,b,c,d being Real st
a<b & c <d & p1`2=d & p2`2= c & a <=p1`1 & p1`1<=b & a<p2`1 & p2`1<=b holds LE
  p1,p2,rectangle(a,b,c,d)
proof
  let p1,p2 be Point of TOP-REAL 2, a,b,c,d be Real;
  set K=rectangle(a,b,c,d);
  assume that
A1: a<b and
A2: c <d and
A3: p1`2=d and
A4: p2`2= c and
A5: a <=p1`1 and
A6: p1`1<= b and
A7: a<p2`1 and
A8: p2`1<=b;
A9: p2 in LSeg(|[b,c]|,|[a,c]|) by A1,A4,A7,A8,Th1;
  W-min K=|[a,c]| by A1,A2,JGRAPH_6:46;
  then
A10: (W-min(K))`1=a by EUCLID:52;
  p1 in LSeg(|[a,d]|,|[b,d]|) by A1,A3,A5,A6,Th1;
  hence thesis by A1,A2,A7,A9,A10,JGRAPH_6:60;
end;
