theorem
  for j be Nat, M be Matrix of n,K st j in Seg n holds Det M = Sum
  LaplaceExpC(M,j)
proof
  let j be Nat, M be Matrix of n,K such that
A1: j in Seg n;
  thus Det M = Det M@ by MATRIXR2:43
    .= Sum LaplaceExpL(M@,j) by A1,Th25
    .= Sum LaplaceExpC(M,j) by A1,Th26;
end;
