theorem Th8:
  for M be lower_triangular Matrix of n,K holds Det M=(the multF of
  K) $$ diagonal_of_Matrix M
proof
  let M be lower_triangular Matrix of n,K;
A1: Det M = Det M@ by MATRIXR2:43;
  M@ is upper_triangular Matrix of n,K by Th2;
  hence Det M= (the multF of K) $$ diagonal_of_Matrix M@ by A1,Th7
    .=(the multF of K) $$ diagonal_of_Matrix M by Th3;
end;
