theorem
  Seg a misses seq(a,b)
proof
  assume Seg a meets seq(a,b);
  then consider a1 being object such that
A1: a1 in Seg a and
A2: a1 in seq(a,b) by XBOOLE_0:3;
  reconsider i = a1 as Element of NAT by A1;
  i <= a & a+1 <= i by A1,A2,Th1,FINSEQ_1:1;
  hence contradiction by NAT_1:13;
end;
