
theorem Th10:
  for p1,p2 being Point of TOP-REAL 2, a,b,c,d being Real
st a<b & c <d & p1`1=b & p2`1=b & c <=p2`2 & p2`2<p1`2 & p1`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`1=b and
A4: p2`1=b and
A5: c <=p2`2 and
A6: p2`2<p1`2 and
A7: p1`2<=d;
  d>=p2`2 by A6,A7,XXREAL_0:2;
  then
A8: p2 in LSeg(|[b,d]|,|[b,c]|) by A2,A4,A5,JGRAPH_6:2;
  p1`2>= c by A5,A6,XXREAL_0:2;
  then p1 in LSeg(|[b,d]|,|[b,c]|) by A2,A3,A7,JGRAPH_6:2;
  hence thesis by A1,A2,A6,A8,JGRAPH_6:61;
end;
