
theorem Th5:
  for p1,p2 being Point of TOP-REAL 2, c,d being Real st p1
  `1<p2`1 & c <d & c <=p1`2 & p1`2<=d & c <=p2`2 & p2`2<=d holds LE p1,p2,
  rectangle(p1`1,p2`1,c,d)
proof
  let p1,p2 be Point of TOP-REAL 2, c,d be Real;
  set a=p1`1, b=p2`1;
  assume that
A1: a<b and
A2: c <d and
A3: c <=p1`2 and
A4: p1`2<=d and
A5: c <=p2`2 and
A6: p2`2<=d;
A7: p2 in LSeg(|[b,c]|,|[b,d]|) by A2,A5,A6,JGRAPH_6:2;
  p1 in LSeg(|[a,c]|,|[a,d]|) by A2,A3,A4,JGRAPH_6:2;
  hence thesis by A1,A2,A7,JGRAPH_6:59;
end;
