proposition: Fact actr_is_action : is_action 'N(A) actr.
proof: Proof. split=> [a u v eq_uv_a | u a b Na Nb]. case Na: (a \in 'N(A)); last by rewrite /actr Na in eq_uv_a. by apply: val_inj; apply: (conjg_inj a); rewrite -!fmvalJ ?eq_uv_a. by apply: val_inj; rewrite !fmvalJ ?groupM ?conjgM. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype bigop ssralg finset fingroup) mathcomp(morphism perm finalg action gproduct commutator) mathcomp(cyclic)