
theorem Th4:
  for p1,p2 being Point of TOP-REAL 2, b,c being Real st p1
  `1<b & c <p2`2 & c <=p1`2 & p1`2<=p2`2 & p1`1<=p2`1 & p2`1<=b holds LE p1,p2,
  rectangle(p1`1,b,c,p2`2)
proof
  let p1,p2 be Point of TOP-REAL 2, b,c be Real;
  set a =p1`1, d=p2`2;
  assume that
A1: a<b and
A2: c <d and
A3: c <=p1`2 and
A4: p1`2<=d and
A5: a<=p2`1 and
A6: p2`1<=b;
A7: p1 in LSeg(|[a,c]|,|[a,d]|) by A2,A3,A4,JGRAPH_6:2;
  p2 in LSeg(|[a,d]|,|[b,d]|) by A1,A5,A6,Th1;
  hence thesis by A1,A2,A7,JGRAPH_6:59;
end;
