
theorem Th3:
  for a,b,d being Real,p being Point of TOP-REAL 2
  st a <=b & p in LSeg(|[a,d]|,|[b,d]|) holds p`2=d & a <=p`1 & p`1<=b
proof
  let a,b,d be Real,p be Point of TOP-REAL 2;
  assume that
A1: a <=b and
A2: p in LSeg(|[a,d]|,|[b,d]|);
  thus p`2=d by A2,TOPREAL3:12;
A3: (|[a,d]|)`1=a by EUCLID:52;
  (|[b,d]|)`1=b by EUCLID:52;
  hence thesis by A1,A2,A3,TOPREAL1:3;
end;
