By the way, you said a bit before that

(A) c' = c(1 + V/c^2)
(B) c' = c(1 + 2V/c^2)
Equation A has a simple derivation.

You did not gave the "simple derivation". Indeed, taking
 f' = f(1+V/c^2)              (1)
 and
f' = c'/L'  ;  f = c/L            (2)

you arrive 2 equations (2) for 3 unknowns (c',L and L'). Then you list
two solutions (out of an infinity)

c' = c(1+V/c^2) ; L' = L   (Einstein 1911)
c' = c ; L' = L/(1+V/c^2)   (anti-Einstein 1911)

From here, I have a certain number of questions ...
1. What is the relation between the $c$ in equation (1) and the one in
equation (2)  ?

2. Should I consider (1) and (2) as a 3 equations system for the
unknowns c,c',f,f',L,L' ?

3. Whatever is the answer to my question 2, one obviously has
infinitely many solutions. Thus, in order to conclude one has to make
use of a new idea.


In light of my question 3, I think that you forgot one or two lines
because you stop your "simple derivation" by just listing two possible
solutions, without even explaining why these two are better than the
inifinitely many others.

Anyway, I guess that I would be able to answer the questions 1-3 by
myself if you just give your derivation of the formula
 f' = f(1+V/c^2)              (1),
on which we agree.


Have a good night
Laurent