proposition: Lemma R1_inj : injective R1.
proof: Proof. by inj_tac; repeat (destruct val => //=; first by apply/eqP). 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)