Corollary 2

Let M be a semiprimordial module. Let $(M_i)_{i\in I}$ and $(M'_j)_{j\in J}$ be families of primordial submodules of M such that

Then there exist an automorphism $u$ of M and a bijection $\varphi$ from I to J such that we have $u(M_i) = M'_{\varphi(i)}$ for every $i\in I$.

For any primordial module L, let $I_L$ (resp. $J_L$) be the set of indices $i\in I$ (resp. $j\in J$) such that $M_i$ (resp. $M'_j$) is isomorphic to L. The nonempty sets of the form $I_L$ (resp. $J_L$) form a partition of I (resp. J), and for every L, we have

Card(I$_L$) $=$ Card(J$_L$) $= [M : L]$;

the corollary follows.