reserve G for Graph,
  k, m, n for Nat;
reserve G for non void Graph;

theorem Th11:
  for f being non empty FinSequence st 1<=m & m<=n & n<=len f
  holds (m,n)-cut f is non empty
proof
  let f be non empty FinSequence;
  set lmn = len (m,n)-cut f;
  assume 1<=m & m<=n & n<=len f;
  then m<n+1 & lmn+m = n+1 by FINSEQ_6:def 4,NAT_1:13;
  then m-(lmn+m)<(n+1)-(n+1) by XREAL_1:9;
  then --lmn>0;
  hence thesis;
end;
