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 Th2:
  for i,j,n being Nat, M being Matrix of n,K st i in dom M holds
  len Deleting(M,i,j) = n-'1
proof
  let i,j,n be Nat, M be Matrix of n,K;
  assume
A1: i in dom M;
A2: len M = n by MATRIX_0:def 2;
  thus len Deleting(M,i,j)= len DelLine(M,i) by MATRIX_0:def 13
    .= n-'1 by A1,A2,Th1;
end;
