reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem
  n>0 implies Det 0_Rmatrix n = 0
proof
  set K=F_Real;
  assume n>0;
  then n>=0+1 by NAT_1:13;
  then Det (0_Rmatrix n)=0.K by MATRIX_7:15
    .=0;
  hence thesis;
end;
