Corollary

The hypotheses and notations being those of Prop. 3, in order that $\Phi'$ be non-degenerate, it is necessary and sufficient that $\Phi$ be non-degenerate.

Indeed, by Prop. 3, we have $(F')^0 = (F^0)'$ and $(E')^0 = (E^0)'$. On the other hand, in order that $\Phi$ (resp. $\Phi'$) be non-degenerate, it is necessary and sufficient that one have $F^0 = E^0 = \{0\}$ (resp. $(F')^0 = (E')^0 = \{0\}$).