End Mod.

(* Specifications: *)
Lemma modact_coset_astab x a :
a \in D -> (to %% 'C(R | to))%act x (coset _ a) = to x a.
Lemma acts_irr_mod_astab G M :
acts_irreducibly G M to ->
acts_irreducibly (G / 'C_G(M | to)) M (mod_groupAction _).