
theorem Th13:
  for p1,p2 being Point of TOP-REAL 2, a,b,c,d being Real
  st a<b & c <d & p1`2= d & p2`1= b & a <=p1`1 & p1`1<=b & c <=p2`2 & p2`2<=d
  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;
  assume that
A1: a<b and
A2: c <d and
A3: p1`2= d and
A4: p2`1= b and
A5: a <=p1`1 and
A6: p1`1<=b and
A7: c <=p2`2 and
A8: p2`2<=d;
A9: p2 in LSeg(|[b,d]|,|[b,c]|) by A2,A4,A7,A8,JGRAPH_6:2;
  p1 in LSeg(|[a,d]|,|[b,d]|) by A1,A3,A5,A6,Th1;
  hence thesis by A1,A2,A9,JGRAPH_6:60;
end;
