theorem Th15:
  for i,j be Nat holds f = <* p,p1,q *> & i<>0 & j>i+1 implies LSeg(f,j) = {}
proof
  let i,j be Nat;
  assume that
A1: f = <* p,p1,q *> and
A2: i<>0 and
A3: j>i+1;
  i>=0+1 by A2,NAT_1:13;
  then 1+i>=1+1 by XREAL_1:7;
  then j>2 by A3,XXREAL_0:2;
  then j>=2+1 by NAT_1:13;
  then
A4: j+1 > 3 by NAT_1:13;
  len f = 3 by A1,FINSEQ_1:45;
  hence thesis by A4,TOPREAL1:def 3;
end;
