proposition: Lemma commg1_sym x y : ([~ x, y] == 1 :> T) = ([~ y, x] == 1 :> T).
proof: Proof. by rewrite -invg_comm (inv_eq invgK) invg1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)