reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th6: ::: NAT_3:5 generalized
  p divides i |^ n implies p divides i
  proof
    assume p divides i|^n;
    then p divides |.i|^n.| by Th4;
    then p divides |.i.| |^ n by TAYLOR_2:1;
    then p divides |.i.| by NAT_3:5;
    hence thesis by Th4;
  end;
