
theorem Th7:
  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=d & a <=p1`1 & p1`1<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;
  assume that
A1: a<b and
A2: c <d and
A3: p1`2=d and
A4: p2`2=d and
A5: a <=p1`1 and
A6: p1`1<p2`1 and
A7: p2`1<=b;
  a<=p2`1 by A5,A6,XXREAL_0:2;
  then
A8: p2 in LSeg(|[a,d]|,|[b,d]|) by A1,A4,A7,Th1;
  p1`1<=b by A6,A7,XXREAL_0:2;
  then p1 in LSeg(|[a,d]|,|[b,d]|) by A1,A3,A5,Th1;
  hence thesis by A1,A2,A6,A8,JGRAPH_6:60;
end;
