Are bond orders always the same in isoelectronic diatomic species?

In my textbook of chemistry it is written that:



> 
> In the Lewis description of covalent bond, the Bond order is given by the number of bonds between the two atoms of a molecule.
>  ... 
>  Isoelectronic molecules and ions have identical bond orders; for example, $\ce{F2}$ and $\ce{O2^{2-}}$ have bond order $1$. $\ce{N2}$, $\ce{CO}$ and $\ce{NO+}$ have bond order $3$. 
> 
> 
> 


I tried some more molecules and it turns out that for two diatomic isoelectronic molecules (neutral or charged) the bond orders are always the same. 


My question is that :


1. If the bond order is always same for isoelectronic species (diatomic molecules and ions) how can I prove it? I tried and got the following result: 


> 
> For any diatomic molecule having combination of elements of same period( either period 2 or period 3) isoelectronic molecules and ions have the same bond order.
> 
> 
>



> 
> Proof: Assume the two atoms $A$ and $B$ ( atoms may be ions also) having valence electrons in their outer shell $x$ and $y$.
>  Now if they combine to form diatomic molecule or ion having bond order $m$ then they must satisfy the below two equation( octet rule):
>  1) $x+m=8$
>  2) $y+m=8$
> 
> 
> Now since they are along same period therefore the total no. of inner electrons( total electrons excluding valence electrons) must be equal( 2 electrons for period 2 elements and 10 electrons for period 3 elements). If we vary the atoms(or ion) $A$ and $B$ the sum of these inner electrons will obviously be constant( equal to 4 electrons for period 2 elements and 20 electrons for period 3 elements).
> 
> 
> Therefore, For species to be isoelectronic:
>  $x+y=constant$( say $k$) 
>  Adding equation 1) and 2) we get:
>  $x+y+2m=16$ or
>  $k+2m=16$ or
>  \*Bond order\*$=m=(16-k)/2$ which is constant. Q.E.D.
> 
> 
> 


2. If the result given in my textbook is not true (since it looks like the fact is universal! compare $\ce{HCl}$ and $\ce{F2}$ which are isoelectronic having same bond order but elements in $\ce{HCl}$ involves period 1 and period 3 elements) then please state any counter examples.


