proposition: Lemma charR H K G : H \char G -> K \char G -> [~: H, K] \char G.
proof: Proof. case/charP=> sHG chH /charP[sKG chK]; apply/charP. by split=> [|f infj Gf]; [rewrite comm_subG | rewrite morphimR // chH // chK]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat fintype) mathcomp(bigop finset binomial fingroup morphism) mathcomp(automorphism quotient gfunctor)