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

theorem Th72:
  Det 1_Rmatrix n=1
proof
  per cases;
  suppose
    n>=1;
    hence Det 1_Rmatrix n=1_(F_Real) by MATRIX_7:16
      .= 1;
  end;
  suppose
    n<1;
    then n=0 by NAT_1:25;
    hence Det (1_Rmatrix n)=1.F_Real by Th41
      .=1;
  end;
end;
