proposition: Lemma isometries_iso : forall p, p \in isometries -> is_iso p.
proof: Proof. move=> p; rewrite inE. by do ?case/orP; move/eqP=> -> a; rewrite !permE; case: a; do 4?case. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype tuple finfun bigop finset fingroup) mathcomp(action perm primitive_action)