reserve x,y for object,
  N for Element of NAT,
  c,i,j,k,m,n for Nat,
  D for non empty set,
  s for Element of 2Set Seg (n+2),
  p for Element of Permutations(n) ,
  p1, q1 for Element of Permutations(n+1),
  p2 for Element of Permutations(n +2),
  K for Field,
  a for Element of K,
  f for FinSequence of K,
  A for (Matrix of K),
  AD for Matrix of n,m,D,
  pD for FinSequence of D,
  M for Matrix of n,K;

theorem Th1:
  for f be FinSequence, i be Nat st i in dom f holds len Del(f,i) = len f -' 1
proof
  let f be FinSequence, i be Nat;
  assume i in dom f;
  then ex m be Nat st len f = m + 1 & len Del(f,i) = m by FINSEQ_3:104;
  hence thesis by NAT_D:34;
end;
