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 Th24:
  for i,j st i in Seg n & j in Seg n holds Minor(M,i,j) = Minor(M@ ,j,i)
proof
  let i,j such that
A1: i in Seg n and
A2: j in Seg n;
  thus Minor(M,i,j) = Det Delete(M,i,j)@ by MATRIXR2:43
    .= Minor(M@,j,i) by A1,A2,Th14;
end;
