reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem
  (k * n) mod k = 0
proof
A0: k is Nat & n is Nat by TARSKI:1;
  per cases;
  suppose k = 0;
    hence thesis by Def2;
  end;
  suppose
A1: k <> 0;
    k * n = k * n + 0;
    hence thesis by A0,A1,Def2;
  end;
end;
